%PDF-1.3 %忏嫌 2 0 obj << /Length 52080 >> stream BT /TT4 1 Tf 12.48 0 0 12.48 90 713 Tm 0 g /GS1 gs 0.0231 Tc 0.2306 Tw (Another derivation of )Tj /TT5 1 Tf 12 0 0 12 223.6031 713 Tm 0 Tc 0 Tw <0067>Tj /TT4 1 Tf 12.48 0 0 12.48 231.0201 713 Tm 0.0148 Tc 0.1486 Tw [( of the parabola r\(1 + cos )]TJ /TT5 1 Tf 12 0 0 12 391.5563 713 Tm 0 Tc 0 Tw <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 398.5973 713 Tm 0.0141 Tc 0.1408 Tw [(\) = 1. Bressoud )]TJ -26.1697 -1.2821 TD 0.0155 Tc 0.1558 Tw [(assumes v = 2. This should be unnecessary. Here is the computation )]TJ T* 0.1031 Tc 0 Tw (without:)Tj 1.4423 -2.5641 TD 0.0233 Tc 0.2333 Tw (Here are two permutations of the original parabola equation: )Tj /TT6 1 Tf 12 0 0 12 90 629 Tm 0 Tc 0 Tw (\()Tj /TT4 1 Tf 12.48 0 0 12.48 94.3721 629 Tm 0.0066 Tc (1 )Tj /TT6 1 Tf 12 0 0 12 105.7592 629 Tm 0 Tc (+)Tj /TT4 1 Tf 12.48 0 0 12.48 112.9641 629 Tm 0.0123 Tc 0.1232 Tw [( cos)]TJ /TT5 1 Tf 12 0 0 12 138.0053 629 Tm 0 Tc 0 Tw <0065>Tj /TT6 1 Tf 0.5612 0 TD (\))Tj /TT4 1 Tf 12.48 0 0 12.48 149.2173 629 Tm ( )Tj /TT6 1 Tf 12 0 0 12 153.0107 629 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 160.2156 629 Tm ( )Tj ET 0 G 0 J 0 j 0.25 w 10 M []0 d 1 i 165 632.875 m 172.25 632.875 l S BT 9.36 0 0 9.36 166 635 Tm (1)Tj 0 -1.4957 TD (r)Tj 12.48 0 0 12.48 174 629 Tm 0.0149 Tc 0.1488 Tw (, cos)Tj /TT5 1 Tf 12 0 0 12 203.1425 629 Tm 0 Tc 0 Tw <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 210.0554 629 Tm ( )Tj /TT6 1 Tf 12 0 0 12 213.8888 629 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 221.1707 629 Tm ( )Tj ET 226 632.875 m 233.25 632.875 l S BT 9.36 0 0 9.36 227 635 Tm (1)Tj T* (r)Tj 12.48 0 0 12.48 235 629 Tm ( )Tj /TT5 1 Tf 12 0 0 12 239.2563 629 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 247.3413 629 Tm 0.0312 Tc 0.3114 Tw [( 1. If we differentiate implicitly we get)]TJ ET 91 606.875 m 102.25 606.875 l S BT 9.36 0 0 9.36 92 609 Tm 0.1797 Tc 0 Tw (dr)Tj T* 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 104 603 Tm 0 Tc (\()Tj /TT4 1 Tf 12.48 0 0 12.48 108.5061 603 Tm 0.0089 Tc (1 )Tj /TT6 1 Tf 12 0 0 12 120.2442 603 Tm 0 Tc (+)Tj /TT4 1 Tf 12.48 0 0 12.48 127.6711 603 Tm 0.0167 Tc 0.1674 Tw [( cos)]TJ /TT5 1 Tf 12 0 0 12 153.4833 603 Tm 0 Tc 0 Tw <0065>Tj /TT6 1 Tf 0.5756 0 TD (\))Tj /TT4 1 Tf 12.48 0 0 12.48 165.0413 603 Tm ( )Tj /TT6 1 Tf 12 0 0 12 168.9517 603 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 176.3786 603 Tm 0.0161 Tc 0.1608 Tw [( rsin)]TJ /TT5 1 Tf 12 0 0 12 202.9673 603 Tm 0 Tc 0 Tw <0065>Tj ET 211 606.875 m 222.25 606.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 212 609 Tm (d)Tj /TT5 1 Tf 9 0 0 9 217.2626 609 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 212 595 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 224 603 Tm 0.0081 Tc 0.0808 Tw (, so )Tj ET 251 606.875 m 262.25 606.875 l S BT 9.36 0 0 9.36 252 609 Tm 0 Tc 0 Tw (d)Tj /TT5 1 Tf 9 0 0 9 257.2626 609 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 252 595 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 264 603 Tm 0 Tc ( )Tj /TT6 1 Tf 12 0 0 12 267.8463 603 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 275.1533 603 Tm ( )Tj ET 280 606.875 m 318.25 606.875 l S BT 9.36 0 0 9.36 281 609 Tm 0.0048 Tc (1 )Tj /TT6 1 Tf 9 0 0 9 289.3481 609 Tm 0 Tc (+)Tj /TT4 1 Tf 9.36 0 0 9.36 294.6305 609 Tm 0.0091 Tc 0.091 Tw [( cos)]TJ /TT5 1 Tf 9 0 0 9 312.9886 609 Tm 0 Tc 0 Tw <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 288 595 Tm 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 305.55 595 Tm 0 Tc <0065>Tj ET 321 606.875 m 332.25 606.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 322 609 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj 12.48 0 0 12.48 334 603 Tm 0 Tc ( )Tj /TT6 1 Tf 12 0 0 12 337.8463 603 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 345.1533 603 Tm ( )Tj ET 350 606.875 m 379.25 606.875 l S BT 9.36 0 0 9.36 362 609 Tm (1)Tj -1.1752 -1.7094 TD (r)Tj 7.28 0 0 7.28 354.6649 598 Tm (2)Tj 9.36 0 0 9.36 359.4258 593 Tm 0.0749 Tc (sin)Tj /TT5 1 Tf 9 0 0 9 373.4938 593 Tm 0 Tc <0065>Tj ET 382 606.875 m 393.25 606.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 383 609 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj 12.48 0 0 12.48 395 603 Tm 0 Tc (.)Tj -24.4391 -3.766 TD 0.0165 Tc 0.1655 Tw (As done in class, v)Tj ET 199 566.875 m 205.25 566.875 l S 203 569 m 203.25 569 l 205.25 567 l 205.25 566.75 l 205 566.75 l 203 568.75 l f 205 567 m 205.25 567 l 205.25 566.75 l 203.25 564.75 l 203 564.75 l 203 565 l f BT 12.48 0 0 12.48 206 556 Tm 0.0028 Tc 0.0283 Tw [( = )]TJ ET 222 559.875 m 233.25 559.875 l S BT 9.36 0 0 9.36 223 562 Tm 0.1797 Tc 0 Tw (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj 12.48 0 0 12.48 235 556 Tm 0 Tc (u)Tj ET 235 566.875 m 241.25 566.875 l S 239 569 m 239.25 569 l 241.25 567 l 241.25 566.75 l 241 566.75 l 239 568.75 l f 241 567 m 241.25 567 l 241.25 566.75 l 239.25 564.75 l 239 564.75 l 239 565 l f BT 9.36 0 0 9.36 242 551 Tm (r)Tj ET 242 558.875 m 246.25 558.875 l S 244 561 m 244.25 561 l 246.25 559 l 246.25 558.75 l 246 558.75 l 244 560.75 l f 246 559 m 246.25 559 l 246.25 558.75 l 244.25 556.75 l 244 556.75 l 244 557 l f BT 12.48 0 0 12.48 247 556 Tm ( )Tj /TT6 1 Tf 12 0 0 12 251.1193 556 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 258.9453 556 Tm 0.1149 Tc ( r)Tj ET 269 559.875 m 280.25 559.875 l S BT 9.36 0 0 9.36 270 562 Tm 0 Tc (d)Tj /TT5 1 Tf 9 0 0 9 275.2626 562 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 270 548 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 282 556 Tm 0 Tc (u)Tj ET 282 566.875 m 288.25 566.875 l S 286 569 m 286.25 569 l 288.25 567 l 288.25 566.75 l 288 566.75 l 286 568.75 l f 288 567 m 288.25 567 l 288.25 566.75 l 286.25 564.75 l 286 564.75 l 286 565 l f BT 9.36 0 0 9.36 289 551 Tm (r)Tj ET 289 558.875 m 293.25 558.875 l S 291 561 m 291.25 561 l 293.25 559 l 293.25 558.75 l 293 558.75 l 291 560.75 l f 293 559 m 293.25 559 l 293.25 558.75 l 291.25 556.75 l 291 556.75 l 291 557 l f BT /TT5 1 Tf 9 0 0 9 294 551 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 300.3978 556 Tm ( )Tj /TT6 1 Tf 12 0 0 12 304.1422 556 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 311.2551 556 Tm ( )Tj ET 316 559.875 m 327.25 559.875 l S BT 9.36 0 0 9.36 317 562 Tm 0.1797 Tc (dr)Tj T* 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 329 548 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj ET q 329 559 6 15 re W n BT 12 0 0 12 329 561 Tm <00a3>Tj ET Q q 329 552 6 9 re W n BT 12 0 0 12 329 556 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 334 556 Tm (u)Tj ET 334 566.875 m 340.25 566.875 l S 338 569 m 338.25 569 l 340.25 567 l 340.25 566.75 l 340 566.75 l 338 568.75 l f 340 567 m 340.25 567 l 340.25 566.75 l 338.25 564.75 l 338 564.75 l 338 565 l f BT 9.36 0 0 9.36 341 551 Tm (r)Tj ET 341 558.875 m 345.25 558.875 l S 343 561 m 343.25 561 l 345.25 559 l 345.25 558.75 l 345 558.75 l 343 560.75 l f 345 559 m 345.25 559 l 345.25 558.75 l 343.25 556.75 l 343 556.75 l 343 557 l f BT 12.48 0 0 12.48 346 556 Tm ( )Tj /TT6 1 Tf 12 0 0 12 349.8463 556 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 357.1533 556 Tm ( )Tj ET 362 559.875 m 386.25 559.875 l S BT 9.36 0 0 9.36 371 562 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 380.55 548 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 388 556 Tm (u)Tj ET 388 566.875 m 394.25 566.875 l S 392 569 m 392.25 569 l 394.25 567 l 394.25 566.75 l 394 566.75 l 392 568.75 l f 394 567 m 394.25 567 l 394.25 566.75 l 392.25 564.75 l 392 564.75 l 392 565 l f BT 9.36 0 0 9.36 395 551 Tm (r)Tj ET 395 558.875 m 399.25 558.875 l S 397 561 m 397.25 561 l 399.25 559 l 399.25 558.75 l 399 558.75 l 397 560.75 l f 399 559 m 399.25 559 l 399.25 558.75 l 397.25 556.75 l 397 556.75 l 397 557 l f BT /TT5 1 Tf 9 0 0 9 400 551 Tm <008c>Tj /TT6 1 Tf 12 0 0 12 405.9748 548 Tm ( )Tj /TT5 1 Tf 0.0021 0 TD <00a6>Tj ET q 406 559 8 15 re W n BT 12 0 0 12 406 561 Tm <00a5>Tj ET Q q 406 552 8 9 re W n BT 12 0 0 12 406 556 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 412 556 Tm 0.0429 Tc ( )Tj -27.2436 -2.8846 TD 0.0071 Tc 0.0703 Tw (and v )Tj /TT6 1 Tf 12 0 0 12 108.281 520 Tm 0 Tc 0 Tw (=)Tj /TT4 1 Tf 12.48 0 0 12.48 115.309 520 Tm ( )Tj ET 120 523.875 m 131.25 523.875 l S BT 9.36 0 0 9.36 121 526 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj 12.48 0 0 12.48 133 520 Tm 0 Tc ( )Tj /TT6 1 Tf 12 0 0 12 136.7533 510 Tm ( )Tj /TT5 1 Tf 0.0206 0 TD <00a4>Tj 0 1.4167 TD <00a3>Tj ET q 137 514 6 13 re W n BT 12 0 0 12 137 518 Tm <00b2>Tj 0 -0.25 TD <00b2>Tj ET Q 144 526 m 144.25 526 l 144.25 525.75 l 143.25 524.75 l 143 524.75 l 143 525 l f 144 526 m 144.25 526 l 147.25 509 l 147.25 508.75 l 147 508.75 l 144 525.75 l f 152 537 m 152.25 537 l 152.25 536.75 l 147.25 508.75 l 147 508.75 l 147 509 l f 152 536.875 m 215.25 536.875 l S BT /TT4 1 Tf 12.48 0 0 12.48 154 520 Tm 0.0087 Tc (1 )Tj /TT6 1 Tf 12 0 0 12 165.7011 520 Tm 0 Tc (+)Tj /TT4 1 Tf 12.48 0 0 12.48 173.105 520 Tm ( )Tj ET 178 523.875 m 212.25 523.875 l S BT 9.36 0 0 9.36 192 526 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 182.6919 515.0001 Tm (2)Tj 9.36 0 0 9.36 187.4877 510 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 201.6608 515.0001 Tm 0 Tc (2)Tj /TT5 1 Tf 9 0 0 9 206.4566 510 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 217 510 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.4167 TD <00a5>Tj ET q 217 514 8 13 re W n BT 12 0 0 12 217 518 Tm <00b4>Tj 0 -0.25 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 223 520 Tm ( )Tj /TT6 1 Tf 12 0 0 12 226.8463 520 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 234.1533 520 Tm ( )Tj ET 239 523.875 m 250.25 523.875 l S BT 9.36 0 0 9.36 240 526 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 252 512 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj 0 1.4167 TD <00a3>Tj ET q 252 516 6 13 re W n BT 12 0 0 12 252 520 Tm <00b2>Tj 0 -0.25 TD <00b2>Tj ET Q 258 523.875 m 340.25 523.875 l S 261 534 m 261.25 534 l 261.25 533.75 l 260.25 532.75 l 260 532.75 l 260 533 l f 261 534 m 261.25 534 l 262.25 525 l 262.25 524.75 l 262 524.75 l 261 533.75 l f 265 539 m 265.25 539 l 265.25 538.75 l 262.25 524.75 l 262 524.75 l 262 525 l f 265 538.875 m 338.25 538.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 268 526 Tm (r)Tj 7.28 0 0 7.28 271.4719 531 Tm (2)Tj /TT6 1 Tf 9 0 0 9 275.9817 526 Tm (\()Tj /TT4 1 Tf 9.36 0 0 9.36 279.3208 526 Tm 0.0079 Tc (1 )Tj /TT5 1 Tf 9 0 0 9 288.0159 526 Tm 0 Tc <003c>Tj /TT4 1 Tf 9.36 0 0 9.36 293.5183 526 Tm 0.015 Tc 0.1492 Tw [( cos)]TJ 7.28 0 0 7.28 312.6414 531 Tm 0 Tc 0 Tw (2)Tj /TT5 1 Tf 9 0 0 9 317.1512 526 Tm <0065>Tj /TT6 1 Tf 0.5743 0 TD 0.0533 Tc (\)+)Tj /TT4 1 Tf 9.36 0 0 9.36 331.2167 526 Tm 0 Tc (1)Tj -4.6172 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 305.55 512 Tm 0 Tc <0065>Tj /TT6 1 Tf 12 0 0 12 342 512 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.4167 TD <00a5>Tj ET q 342 516 8 13 re W n BT 12 0 0 12 342 520 Tm <00b4>Tj 0 -0.25 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 348 520 Tm ( )Tj /TT6 1 Tf 12 0 0 12 351.8463 520 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 359.1533 520 Tm ( )Tj ET 364 523.875 m 375.25 523.875 l S BT 9.36 0 0 9.36 365 526 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 377 512 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj 0 1.4167 TD <00a3>Tj ET q 377 516 6 13 re W n BT 12 0 0 12 377 520 Tm <00b2>Tj 0 -0.25 TD <00b2>Tj ET Q 383 523.875 m 503.25 523.875 l S 386 534 m 386.25 534 l 386.25 533.75 l 385.25 532.75 l 385 532.75 l 385 533 l f 386 534 m 386.25 534 l 387.25 525 l 387.25 524.75 l 387 524.75 l 386 533.75 l f 390 539 m 390.25 539 l 390.25 538.75 l 387.25 524.75 l 387 524.75 l 387 525 l f 390 538.875 m 501.25 538.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 393 526 Tm (r)Tj 7.28 0 0 7.28 396.386 531 Tm (2)Tj /TT6 1 Tf 9 0 0 9 400.7848 526 Tm (\()Tj /TT4 1 Tf 9.36 0 0 9.36 404.0408 526 Tm 0.006 Tc (1 )Tj /TT5 1 Tf 9 0 0 9 412.5209 526 Tm 0 Tc <003c>Tj /TT4 1 Tf 9.36 0 0 9.36 417.8874 526 Tm 0.0113 Tc 0.1133 Tw [( cos)]TJ /TT5 1 Tf 9 0 0 9 436.5375 526 Tm 0 Tc 0 Tw <0065>Tj /TT6 1 Tf 0.5552 0 TD 0.0342 Tc (\)\()Tj /TT4 1 Tf 9.36 0 0 9.36 448.1446 526 Tm 0.006 Tc (1 )Tj /TT6 1 Tf 9 0 0 9 456.6247 526 Tm 0 Tc (+)Tj /TT4 1 Tf 9.36 0 0 9.36 461.9911 526 Tm 0.0113 Tc 0.1133 Tw [( cos)]TJ /TT5 1 Tf 9 0 0 9 480.6412 526 Tm 0 Tc 0 Tw <0065>Tj /TT6 1 Tf 0.5614 0 TD 0.0404 Tc (\)+)Tj /TT4 1 Tf 9.36 0 0 9.36 494.3587 526 Tm 0 Tc (1)Tj -6.6623 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 449.55 512 Tm 0 Tc <0065>Tj /TT6 1 Tf 12 0 0 12 505 512 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.4167 TD <00a5>Tj ET q 505 516 8 13 re W n BT 12 0 0 12 505 520 Tm <00b4>Tj 0 -0.25 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 511 520 Tm ( )Tj /TT6 1 Tf 12 0 0 12 514.8463 520 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 522.1533 520 Tm ( )Tj ET 73 473.875 m 84.25 473.875 l S BT 9.36 0 0 9.36 74 476 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 86 462 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj 0 2.4167 TD <00a3>Tj 0 -1.75 TD <00b2>Tj ET q 86 466 6 25 re W n BT 12 0 0 12 86 482 Tm <00b2>Tj ET Q BT 12 0 0 12 86 479 Tm <00b2>Tj ET q 86 466 6 25 re W n BT 12 0 0 12 86 467 Tm <00b2>Tj ET Q 92 473.875 m 180.25 473.875 l S 95 491 m 95.25 491 l 95.25 490.75 l 94.25 489.75 l 94 489.75 l 94 490 l f 95 491 m 95.25 491 l 96.25 475 l 96.25 474.75 l 96 474.75 l 95 490.75 l f 99 501 m 99.25 501 l 99.25 500.75 l 96.25 474.75 l 96 474.75 l 96 475 l f 99 500.875 m 178.25 500.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 102 484 Tm (r)Tj /TT6 1 Tf 9 0 0 9 106.6469 478 Tm ( )Tj /TT5 1 Tf 0.0392 0 TD <00a4>Tj ET q 107 487 5 12 re W n BT 9 0 0 9 107 489 Tm <00a3>Tj ET Q q 107 482 5 7 re W n BT 9 0 0 9 107 485 Tm <00b2>Tj 0 -0.5556 TD <00b2>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 111 484 Tm 0.0095 Tc (1 )Tj /TT5 1 Tf 9 0 0 9 119.8731 484 Tm 0 Tc <003c>Tj /TT4 1 Tf 9.36 0 0 9.36 125.4885 484 Tm ( )Tj /TT6 1 Tf 9 0 0 9 128.4441 481 Tm ( )Tj ET q 128 478 5 9 re W n BT /TT5 1 Tf 9 0 0 9 128 481 Tm <00a4>Tj ET Q q 128 487 5 9 re W n BT /TT5 1 Tf 9 0 0 9 128 486 Tm <00a3>Tj ET Q 133 486.875 m 139.25 486.875 l S BT /TT4 1 Tf 7.28 0 0 7.28 134 490 Tm (1)Tj 0.1374 -1.3736 TD (r)Tj 9.36 0 0 9.36 141 484 Tm ( )Tj /TT5 1 Tf 9 0 0 9 143.9555 484 Tm <003c>Tj /TT4 1 Tf 9.36 0 0 9.36 149.571 484 Tm 0.1045 Tc ( 1)Tj /TT6 1 Tf 9 0 0 9 158.4441 481 Tm 0 Tc ( )Tj ET q 158 478 6 9 re W n BT /TT5 1 Tf 9 0 0 9 158 481 Tm <00a6>Tj ET Q q 158 487 6 9 re W n BT /TT5 1 Tf 9 0 0 9 158 486 Tm <00a5>Tj ET Q BT 9 0 0 9 162 478 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 162 487 6 12 re W n BT 9 0 0 9 162 489 Tm <00a5>Tj ET Q q 162 482 6 7 re W n BT 9 0 0 9 162 485 Tm <00b4>Tj 0 -0.5556 TD <00b4>Tj ET Q BT /TT6 1 Tf 9 0 0 9 166 484 Tm (+)Tj /TT4 1 Tf 9.36 0 0 9.36 171.3564 484 Tm (1)Tj -4.9526 -2.3504 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 142.55 462 Tm 0 Tc <0065>Tj /TT6 1 Tf 12 0 0 12 182 462 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 2.4167 TD <00a5>Tj 0 -1.75 TD <00b4>Tj ET q 182 466 8 25 re W n BT 12 0 0 12 182 482 Tm <00b4>Tj ET Q BT 12 0 0 12 182 479 Tm <00b4>Tj ET q 182 466 8 25 re W n BT 12 0 0 12 182 467 Tm <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 188 470 Tm ( )Tj /TT6 1 Tf 12 0 0 12 191.8463 470 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 199.1533 470 Tm ( )Tj ET 204 473.875 m 215.25 473.875 l S BT 9.36 0 0 9.36 205 476 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj ET 218 473.875 m 254.25 473.875 l S 229 482 m 229.25 482 l 229.25 481.75 l 228.25 480.75 l 228 480.75 l 228 481 l f 229 482 m 229.25 482 l 230.25 475 l 230.25 474.75 l 230 474.75 l 229 481.75 l f 233 487 m 233.25 487 l 233.25 486.75 l 230.25 474.75 l 230 474.75 l 230 475 l f 233 486.875 m 243.25 486.875 l S BT 9.36 0 0 9.36 236 476 Tm 0 Tc (2)Tj ET 221 466 m 221.25 466 l 221.25 465.75 l 220.25 464.75 l 220 464.75 l 220 465 l f 221 466 m 221.25 466 l 222.25 459 l 222.25 458.75 l 222 458.75 l 221 465.75 l f 225 471 m 225.25 471 l 225.25 470.75 l 222.25 458.75 l 222 458.75 l 222 459 l f 225 470.875 m 234.25 470.875 l S BT 9.36 0 0 9.36 228 460 Tm 0.0345 Tc [(r)-487.2(sin)]TJ /TT5 1 Tf 9 0 0 9 248.9341 460 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 256 470 Tm (.)Tj -13.3013 -3.2853 TD 0.0322 Tc 0.3219 Tw (We differentiate to find )Tj 0 -1.8429 TD 0 Tc 0 Tw (a)Tj ET 90 416.875 m 96.25 416.875 l S 94 419 m 94.25 419 l 96.25 417 l 96.25 416.75 l 96 416.75 l 94 418.75 l f 96 417 m 96.25 417 l 96.25 416.75 l 94.25 414.75 l 94 414.75 l 94 415 l f BT 12.48 0 0 12.48 97 406 Tm ( )Tj /TT6 1 Tf 12 0 0 12 100.8463 406 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 108.1533 406 Tm ( )Tj ET 113 409.875 m 125.25 409.875 l S BT 9.36 0 0 9.36 114 412 Tm 0.1193 Tc (dv)Tj ET 119 419.875 m 124.25 419.875 l S 122 422 m 122.25 422 l 124.25 420 l 124.25 419.75 l 124 419.75 l 122 421.75 l f 124 420 m 124.25 420 l 124.25 419.75 l 122.25 417.75 l 122 417.75 l 122 418 l f BT 9.36 0 0 9.36 115 398 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 127 406 Tm 0 Tc ( )Tj /TT6 1 Tf 12 0 0 12 130.7943 406 Tm (=)Tj ET 139 409.875 m 155.25 409.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 140 412 Tm (d)Tj 7.28 0 0 7.28 146.3146 417 Tm (2)Tj 9.36 0 0 9.36 151.2254 412 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 149.2221 401 Tm 0 Tc (2)Tj /TT6 1 Tf 12 0 0 12 157 398 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj ET q 157 409 6 15 re W n BT 12 0 0 12 157 411 Tm <00a3>Tj ET Q q 157 402 6 9 re W n BT 12 0 0 12 157 406 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 162 406 Tm (u)Tj ET 162 416.875 m 168.25 416.875 l S 166 419 m 166.25 419 l 168.25 417 l 168.25 416.75 l 168 416.75 l 166 418.75 l f 168 417 m 168.25 417 l 168.25 416.75 l 166.25 414.75 l 166 414.75 l 166 415 l f BT 9.36 0 0 9.36 169 401 Tm (r)Tj ET 169 408.875 m 173.25 408.875 l S 171 411 m 171.25 411 l 173.25 409 l 173.25 408.75 l 173 408.75 l 171 410.75 l f 173 409 m 173.25 409 l 173.25 408.75 l 171.25 406.75 l 171 406.75 l 171 407 l f BT 12.48 0 0 12.48 174 406 Tm ( )Tj /TT6 1 Tf 12 0 0 12 177.8463 406 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 185.1533 406 Tm ( )Tj ET 190 409.875 m 214.25 409.875 l S BT 9.36 0 0 9.36 199 412 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 208.55 398 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 216 406 Tm (u)Tj ET 216 416.875 m 222.25 416.875 l S 220 419 m 220.25 419 l 222.25 417 l 222.25 416.75 l 222 416.75 l 220 418.75 l f 222 417 m 222.25 417 l 222.25 416.75 l 220.25 414.75 l 220 414.75 l 220 415 l f BT 9.36 0 0 9.36 223 401 Tm (r)Tj ET 223 408.875 m 227.25 408.875 l S 225 411 m 225.25 411 l 227.25 409 l 227.25 408.75 l 227 408.75 l 225 410.75 l f 227 409 m 227.25 409 l 227.25 408.75 l 225.25 406.75 l 225 406.75 l 225 407 l f BT /TT5 1 Tf 9 0 0 9 228 401 Tm <008c>Tj /TT6 1 Tf 12 0 0 12 233.9748 398 Tm ( )Tj /TT5 1 Tf 0.0021 0 TD <00a6>Tj ET q 234 409 8 15 re W n BT 12 0 0 12 234 411 Tm <00a5>Tj ET Q q 234 402 8 9 re W n BT 12 0 0 12 234 406 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 240 406 Tm ( )Tj /TT6 1 Tf 12 0 0 12 243.8463 406 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 251.1533 406 Tm ( )Tj ET 256 409.875 m 267.25 409.875 l S BT 9.36 0 0 9.36 257 412 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 269 396 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj 0 1.25 TD <00a3>Tj ET q 269 400 6 11 re W n BT 12 0 0 12 269 404 Tm <00b2>Tj 0 -0.4167 TD <00b2>Tj ET Q 275 409.875 m 286.25 409.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 276 412 Tm (d)Tj /TT5 1 Tf 9 0 0 9 281.2626 412 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 276 398 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 288 406 Tm 0 Tc (u)Tj ET 288 416.875 m 294.25 416.875 l S 292 419 m 292.25 419 l 294.25 417 l 294.25 416.75 l 294 416.75 l 292 418.75 l f 294 417 m 294.25 417 l 294.25 416.75 l 292.25 414.75 l 292 414.75 l 292 415 l f BT 9.36 0 0 9.36 295 401 Tm (r)Tj ET 295 408.875 m 299.25 408.875 l S 297 411 m 297.25 411 l 299.25 409 l 299.25 408.75 l 299 408.75 l 297 410.75 l f 299 409 m 299.25 409 l 299.25 408.75 l 297.25 406.75 l 297 406.75 l 297 407 l f BT /TT5 1 Tf 9 0 0 9 300 401 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 306.3978 406 Tm ( )Tj /TT5 1 Tf 12 0 0 12 310.1422 406 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 317.2551 406 Tm ( )Tj ET 322 409.875 m 351.25 409.875 l S BT 9.36 0 0 9.36 334 412 Tm (1)Tj -1.1752 -1.7094 TD (r)Tj 7.28 0 0 7.28 326.6649 401 Tm (2)Tj 9.36 0 0 9.36 331.4257 396 Tm 0.0749 Tc (sin)Tj /TT5 1 Tf 9 0 0 9 345.4938 396 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 353 406 Tm (u)Tj ET 353 416.875 m 359.25 416.875 l S 357 419 m 357.25 419 l 359.25 417 l 359.25 416.75 l 359 416.75 l 357 418.75 l f 359 417 m 359.25 417 l 359.25 416.75 l 357.25 414.75 l 357 414.75 l 357 415 l f BT 9.36 0 0 9.36 360 401 Tm (r)Tj ET 360 408.875 m 364.25 408.875 l S 362 411 m 362.25 411 l 364.25 409 l 364.25 408.75 l 364 408.75 l 362 410.75 l f 364 409 m 364.25 409 l 364.25 408.75 l 362.25 406.75 l 362 406.75 l 362 407 l f BT /TT5 1 Tf 9 0 0 9 365 401 Tm <008c>Tj ET 372 409.875 m 383.25 409.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 373 412 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj 12.48 0 0 12.48 385 406 Tm 0 Tc ( )Tj /TT5 1 Tf 12 0 0 12 388.8463 406 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 396.1533 406 Tm ( )Tj ET 401 409.875 m 430.25 409.875 l S BT 9.36 0 0 9.36 406 412 Tm 0.0202 Tc (cos)Tj /TT5 1 Tf 9 0 0 9 421.1326 412 Tm 0 Tc <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 402 396 Tm 0.0708 Tc (rsin)Tj 7.28 0 0 7.28 419.734 401 Tm 0 Tc (2)Tj /TT5 1 Tf 9 0 0 9 424.4948 396 Tm <0065>Tj ET 433 409.875 m 444.25 409.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 434 412 Tm (d)Tj /TT5 1 Tf 9 0 0 9 439.2626 412 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 434 398 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 446 406 Tm 0 Tc (u)Tj ET 446 416.875 m 452.25 416.875 l S 450 419 m 450.25 419 l 452.25 417 l 452.25 416.75 l 452 416.75 l 450 418.75 l f 452 417 m 452.25 417 l 452.25 416.75 l 450.25 414.75 l 450 414.75 l 450 415 l f BT 9.36 0 0 9.36 453 401 Tm (r)Tj ET 453 408.875 m 457.25 408.875 l S 455 411 m 455.25 411 l 457.25 409 l 457.25 408.75 l 457 408.75 l 455 410.75 l f 457 409 m 457.25 409 l 457.25 408.75 l 455.25 406.75 l 455 406.75 l 455 407 l f BT /TT5 1 Tf 9 0 0 9 458 401 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 464.3978 406 Tm ( )Tj /TT5 1 Tf 12 0 0 12 468.1422 406 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 475.2551 406 Tm ( )Tj ET 480 409.875 m 504.25 409.875 l S BT 9.36 0 0 9.36 489 412 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 498.55 398 Tm 0 Tc <0065>Tj ET 507 409.875 m 518.25 409.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 508 412 Tm (d)Tj /TT5 1 Tf 9 0 0 9 513.2626 412 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 508 398 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 520 406 Tm 0 Tc (u)Tj ET 520 416.875 m 526.25 416.875 l S 524 419 m 524.25 419 l 526.25 417 l 526.25 416.75 l 526 416.75 l 524 418.75 l f 526 417 m 526.25 417 l 526.25 416.75 l 524.25 414.75 l 524 414.75 l 524 415 l f BT 9.36 0 0 9.36 527 401 Tm (r)Tj ET 527 408.875 m 531.25 408.875 l S 529 411 m 529.25 411 l 531.25 409 l 531.25 408.75 l 531 408.75 l 529 410.75 l f 531 409 m 531.25 409 l 531.25 408.75 l 529.25 406.75 l 529 406.75 l 529 407 l f BT /TT6 1 Tf 12 0 0 12 532 396 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.25 TD <00a5>Tj ET q 532 400 8 11 re W n BT 12 0 0 12 532 404 Tm <00b4>Tj 0 -0.4167 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 90 375 Tm 0.0301 Tc (Coverting )Tj ET 155 378.875 m 166.25 378.875 l S BT 9.36 0 0 9.36 156 381 Tm 0 Tc (d)Tj /TT5 1 Tf 9 0 0 9 161.2626 381 Tm <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 156 367 Tm 0.1278 Tc (dt)Tj 12.48 0 0 12.48 168 375 Tm 0.0191 Tc 0.1908 Tw [( into )]TJ ET 202 378.875 m 213.25 378.875 l S BT 9.36 0 0 9.36 203 381 Tm 0.1797 Tc 0 Tw (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj 12.48 0 0 12.48 215 375 Tm 0.0188 Tc 0.1871 Tw [(, we get)]TJ /TT6 1 Tf 12 0 0 12 90 342 Tm 0 Tc 0 Tw (=)Tj ET 98 345.875 m 114.25 345.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 99 348 Tm (d)Tj 7.28 0 0 7.28 105.3146 353 Tm (2)Tj 9.36 0 0 9.36 110.2254 348 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 108.2221 337 Tm 0 Tc (2)Tj /TT6 1 Tf 12 0 0 12 116 334 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj ET q 116 345 6 15 re W n BT 12 0 0 12 116 347 Tm <00a3>Tj ET Q q 116 338 6 9 re W n BT 12 0 0 12 116 342 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 121 342 Tm (u)Tj ET 121 352.875 m 127.25 352.875 l S 125 355 m 125.25 355 l 127.25 353 l 127.25 352.75 l 127 352.75 l 125 354.75 l f 127 353 m 127.25 353 l 127.25 352.75 l 125.25 350.75 l 125 350.75 l 125 351 l f BT 9.36 0 0 9.36 128 337 Tm (r)Tj ET 128 344.875 m 132.25 344.875 l S 130 347 m 130.25 347 l 132.25 345 l 132.25 344.75 l 132 344.75 l 130 346.75 l f 132 345 m 132.25 345 l 132.25 344.75 l 130.25 342.75 l 130 342.75 l 130 343 l f BT 12.48 0 0 12.48 133 342 Tm ( )Tj /TT6 1 Tf 12 0 0 12 136.8463 342 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 144.1533 342 Tm ( )Tj ET 149 345.875 m 173.25 345.875 l S BT 9.36 0 0 9.36 158 348 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 167.55 334 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 175 342 Tm (u)Tj ET 175 352.875 m 181.25 352.875 l S 179 355 m 179.25 355 l 181.25 353 l 181.25 352.75 l 181 352.75 l 179 354.75 l f 181 353 m 181.25 353 l 181.25 352.75 l 179.25 350.75 l 179 350.75 l 179 351 l f BT 9.36 0 0 9.36 182 337 Tm (r)Tj ET 182 344.875 m 186.25 344.875 l S 184 347 m 184.25 347 l 186.25 345 l 186.25 344.75 l 186 344.75 l 184 346.75 l f 186 345 m 186.25 345 l 186.25 344.75 l 184.25 342.75 l 184 342.75 l 184 343 l f BT /TT5 1 Tf 9 0 0 9 187 337 Tm <008c>Tj /TT6 1 Tf 12 0 0 12 192.9748 334 Tm ( )Tj /TT5 1 Tf 0.0021 0 TD <00a6>Tj ET q 193 345 8 15 re W n BT 12 0 0 12 193 347 Tm <00a5>Tj ET Q q 193 338 8 9 re W n BT 12 0 0 12 193 342 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 199 342 Tm ( )Tj /TT6 1 Tf 12 0 0 12 202.7773 342 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 209.9533 342 Tm ( )Tj /TT6 1 Tf 12 0 0 12 213.7306 334 Tm ( )Tj /TT5 1 Tf 0.0225 0 TD <00a4>Tj ET q 214 345 6 15 re W n BT 12 0 0 12 214 347 Tm <00a3>Tj ET Q q 214 338 6 9 re W n BT 12 0 0 12 214 342 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q 220 345.875 m 231.25 345.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 221 348 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 233 334 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 233 345 8 15 re W n BT 12 0 0 12 233 347 Tm <00a5>Tj ET Q q 233 338 8 9 re W n BT 12 0 0 12 233 342 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 239 355 Tm (2)Tj /TT6 1 Tf 12 0 0 12 244.7106 332 Tm ( )Tj /TT5 1 Tf 0.0241 0 TD <00a4>Tj 0 1.25 TD <00a3>Tj ET q 245 336 6 11 re W n BT 12 0 0 12 245 340 Tm <00b2>Tj 0 -0.4167 TD <00b2>Tj ET Q 251 345.875 m 280.25 345.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 263 348 Tm (1)Tj -1.1752 -1.7094 TD (r)Tj 7.28 0 0 7.28 255.6649 337 Tm (2)Tj 9.36 0 0 9.36 260.4257 332 Tm 0.0749 Tc (sin)Tj /TT5 1 Tf 9 0 0 9 274.4938 332 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 282 342 Tm (u)Tj ET 282 352.875 m 288.25 352.875 l S 286 355 m 286.25 355 l 288.25 353 l 288.25 352.75 l 288 352.75 l 286 354.75 l f 288 353 m 288.25 353 l 288.25 352.75 l 286.25 350.75 l 286 350.75 l 286 351 l f BT 9.36 0 0 9.36 289 337 Tm (r)Tj ET 289 344.875 m 293.25 344.875 l S 291 347 m 291.25 347 l 293.25 345 l 293.25 344.75 l 293 344.75 l 291 346.75 l f 293 345 m 293.25 345 l 293.25 344.75 l 291.25 342.75 l 291 342.75 l 291 343 l f BT /TT5 1 Tf 9 0 0 9 294 337 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 300.3978 342 Tm ( )Tj /TT5 1 Tf 12 0 0 12 304.1422 342 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 311.2551 342 Tm ( )Tj ET 316 345.875 m 345.25 345.875 l S BT 9.36 0 0 9.36 328 348 Tm (1)Tj -1.1752 -1.7094 TD (r)Tj 7.28 0 0 7.28 320.6649 337 Tm (2)Tj 9.36 0 0 9.36 325.4257 332 Tm 0.0749 Tc (sin)Tj /TT5 1 Tf 9 0 0 9 339.4938 332 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 347 342 Tm (u)Tj ET 347 352.875 m 353.25 352.875 l S 351 355 m 351.25 355 l 353.25 353 l 353.25 352.75 l 353 352.75 l 351 354.75 l f 353 353 m 353.25 353 l 353.25 352.75 l 351.25 350.75 l 351 350.75 l 351 351 l f BT 9.36 0 0 9.36 354 337 Tm (r)Tj ET 354 344.875 m 358.25 344.875 l S 356 347 m 356.25 347 l 358.25 345 l 358.25 344.75 l 358 344.75 l 356 346.75 l f 358 345 m 358.25 345 l 358.25 344.75 l 356.25 342.75 l 356 342.75 l 356 343 l f BT /TT5 1 Tf 9 0 0 9 359 337 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 365.3978 342 Tm ( )Tj /TT5 1 Tf 12 0 0 12 369.1422 342 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 376.2551 342 Tm ( )Tj ET 381 345.875 m 415.25 345.875 l S BT 9.36 0 0 9.36 388 348 Tm 0.0202 Tc (cos)Tj /TT5 1 Tf 9 0 0 9 403.1326 348 Tm 0 Tc <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 382 332 Tm (r)Tj 7.28 0 0 7.28 385.692 337 Tm (3)Tj 9.36 0 0 9.36 390.4877 332 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 404.6608 337 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 409.4566 332 Tm <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 417 342 Tm (u)Tj ET 417 352.875 m 423.25 352.875 l S 421 355 m 421.25 355 l 423.25 353 l 423.25 352.75 l 423 352.75 l 421 354.75 l f 423 353 m 423.25 353 l 423.25 352.75 l 421.25 350.75 l 421 350.75 l 421 351 l f BT 9.36 0 0 9.36 424 337 Tm (r)Tj ET 424 344.875 m 428.25 344.875 l S 426 347 m 426.25 347 l 428.25 345 l 428.25 344.75 l 428 344.75 l 426 346.75 l f 428 345 m 428.25 345 l 428.25 344.75 l 426.25 342.75 l 426 342.75 l 426 343 l f BT /TT5 1 Tf 9 0 0 9 429 337 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 435.3978 342 Tm ( )Tj /TT5 1 Tf 12 0 0 12 439.1422 342 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 446.2551 342 Tm ( )Tj ET 451 345.875 m 485.25 345.875 l S BT 9.36 0 0 9.36 465 348 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 455.692 337 Tm (3)Tj 9.36 0 0 9.36 460.4877 332 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 474.6608 337 Tm 0 Tc (2)Tj /TT5 1 Tf 9 0 0 9 479.4566 332 Tm <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 487 342 Tm (u)Tj ET 487 352.875 m 493.25 352.875 l S 491 355 m 491.25 355 l 493.25 353 l 493.25 352.75 l 493 352.75 l 491 354.75 l f 493 353 m 493.25 353 l 493.25 352.75 l 491.25 350.75 l 491 350.75 l 491 351 l f BT 9.36 0 0 9.36 494 337 Tm (r)Tj ET 494 344.875 m 498.25 344.875 l S 496 347 m 496.25 347 l 498.25 345 l 498.25 344.75 l 498 344.75 l 496 346.75 l f 498 345 m 498.25 345 l 498.25 344.75 l 496.25 342.75 l 496 342.75 l 496 343 l f BT /TT6 1 Tf 12 0 0 12 499 332 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.25 TD <00a5>Tj ET q 499 336 8 11 re W n BT 12 0 0 12 499 340 Tm <00b4>Tj 0 -0.4167 TD <00b4>Tj ET Q BT /TT6 1 Tf 12 0 0 12 90 304 Tm (=)Tj ET 98 307.875 m 114.25 307.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 99 310 Tm (d)Tj 7.28 0 0 7.28 105.3146 315 Tm (2)Tj 9.36 0 0 9.36 110.2254 310 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 108.2221 299 Tm 0 Tc (2)Tj /TT6 1 Tf 12 0 0 12 116 296 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj ET q 116 307 6 15 re W n BT 12 0 0 12 116 309 Tm <00a3>Tj ET Q q 116 300 6 9 re W n BT 12 0 0 12 116 304 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 121 304 Tm (u)Tj ET 121 314.875 m 127.25 314.875 l S 125 317 m 125.25 317 l 127.25 315 l 127.25 314.75 l 127 314.75 l 125 316.75 l f 127 315 m 127.25 315 l 127.25 314.75 l 125.25 312.75 l 125 312.75 l 125 313 l f BT 9.36 0 0 9.36 128 299 Tm (r)Tj ET 128 306.875 m 132.25 306.875 l S 130 309 m 130.25 309 l 132.25 307 l 132.25 306.75 l 132 306.75 l 130 308.75 l f 132 307 m 132.25 307 l 132.25 306.75 l 130.25 304.75 l 130 304.75 l 130 305 l f BT 12.48 0 0 12.48 133 304 Tm ( )Tj /TT6 1 Tf 12 0 0 12 136.8463 304 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 144.1533 304 Tm ( )Tj ET 149 307.875 m 173.25 307.875 l S BT 9.36 0 0 9.36 158 310 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 167.55 296 Tm 0 Tc <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 175 304 Tm (u)Tj ET 175 314.875 m 181.25 314.875 l S 179 317 m 179.25 317 l 181.25 315 l 181.25 314.75 l 181 314.75 l 179 316.75 l f 181 315 m 181.25 315 l 181.25 314.75 l 179.25 312.75 l 179 312.75 l 179 313 l f BT 9.36 0 0 9.36 182 299 Tm (r)Tj ET 182 306.875 m 186.25 306.875 l S 184 309 m 184.25 309 l 186.25 307 l 186.25 306.75 l 186 306.75 l 184 308.75 l f 186 307 m 186.25 307 l 186.25 306.75 l 184.25 304.75 l 184 304.75 l 184 305 l f BT /TT5 1 Tf 9 0 0 9 187 299 Tm <008c>Tj /TT6 1 Tf 12 0 0 12 192.9748 296 Tm ( )Tj /TT5 1 Tf 0.0021 0 TD <00a6>Tj ET q 193 307 8 15 re W n BT 12 0 0 12 193 309 Tm <00a5>Tj ET Q q 193 300 8 9 re W n BT 12 0 0 12 193 304 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 199 304 Tm ( )Tj /TT6 1 Tf 12 0 0 12 202.7773 304 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 209.9533 304 Tm ( )Tj /TT6 1 Tf 12 0 0 12 213.7306 296 Tm ( )Tj /TT5 1 Tf 0.0225 0 TD <00a4>Tj ET q 214 307 6 15 re W n BT 12 0 0 12 214 309 Tm <00a3>Tj ET Q q 214 300 6 9 re W n BT 12 0 0 12 214 304 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q 220 307.875 m 231.25 307.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 221 310 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 233 296 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 233 307 8 15 re W n BT 12 0 0 12 233 309 Tm <00a5>Tj ET Q q 233 300 8 9 re W n BT 12 0 0 12 233 304 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 239 317 Tm (2)Tj /TT6 1 Tf 12 0 0 12 244.7106 294 Tm ( )Tj /TT5 1 Tf 0.0241 0 TD <00a4>Tj 0 1.25 TD <00a3>Tj ET q 245 298 6 11 re W n BT 12 0 0 12 245 302 Tm <00b2>Tj 0 -0.4167 TD <00b2>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 250 304 Tm ()Tj /TT5 1 Tf 12 0 0 12 257.4917 304 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 263.1096 304 Tm ( )Tj ET 262 307.875 m 296.25 307.875 l S BT 9.36 0 0 9.36 269 310 Tm 0.0202 Tc (cos)Tj /TT5 1 Tf 9 0 0 9 284.1326 310 Tm 0 Tc <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 263 294 Tm (r)Tj 7.28 0 0 7.28 266.692 299 Tm (3)Tj 9.36 0 0 9.36 271.4877 294 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 285.6608 299 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 290.4566 294 Tm <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 298 304 Tm (u)Tj ET 298 314.875 m 304.25 314.875 l S 302 317 m 302.25 317 l 304.25 315 l 304.25 314.75 l 304 314.75 l 302 316.75 l f 304 315 m 304.25 315 l 304.25 314.75 l 302.25 312.75 l 302 312.75 l 302 313 l f BT 9.36 0 0 9.36 305 299 Tm (r)Tj ET 305 306.875 m 309.25 306.875 l S 307 309 m 307.25 309 l 309.25 307 l 309.25 306.75 l 309 306.75 l 307 308.75 l f 309 307 m 309.25 307 l 309.25 306.75 l 307.25 304.75 l 307 304.75 l 307 305 l f BT /TT5 1 Tf 9 0 0 9 310 299 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 316.3978 304 Tm ( )Tj /TT5 1 Tf 12 0 0 12 320.1422 304 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 327.2551 304 Tm ( )Tj ET 332 307.875 m 366.25 307.875 l S BT 9.36 0 0 9.36 346 310 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 336.692 299 Tm (3)Tj 9.36 0 0 9.36 341.4877 294 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 355.6608 299 Tm 0 Tc (2)Tj /TT5 1 Tf 9 0 0 9 360.4566 294 Tm <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 368 304 Tm (u)Tj ET 368 314.875 m 374.25 314.875 l S 372 317 m 372.25 317 l 374.25 315 l 374.25 314.75 l 374 314.75 l 372 316.75 l f 374 315 m 374.25 315 l 374.25 314.75 l 372.25 312.75 l 372 312.75 l 372 313 l f BT 9.36 0 0 9.36 375 299 Tm (r)Tj ET 375 306.875 m 379.25 306.875 l S 377 309 m 377.25 309 l 379.25 307 l 379.25 306.75 l 379 306.75 l 377 308.75 l f 379 307 m 379.25 307 l 379.25 306.75 l 377.25 304.75 l 377 304.75 l 377 305 l f BT /TT6 1 Tf 12 0 0 12 380 294 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.25 TD <00a5>Tj ET q 380 298 8 11 re W n BT 12 0 0 12 380 302 Tm <00b4>Tj 0 -0.4167 TD <00b4>Tj ET Q BT /TT6 1 Tf 12 0 0 12 90 268.0001 Tm (=)Tj 0.5726 -0.8333 TD ( )Tj /TT5 1 Tf 0.0108 0 TD <00a4>Tj 0 1.4167 TD <00a3>Tj ET q 97 262 6 13 re W n BT 12 0 0 12 97 266 Tm <00b2>Tj 0 -0.25 TD <00b2>Tj ET Q 103 271.875 m 119.25 271.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 104 274 Tm (d)Tj 7.28 0 0 7.28 110.3146 279 Tm (2)Tj 9.36 0 0 9.36 115.2254 274 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 113.2221 263 Tm 0 Tc (2)Tj 12.48 0 0 12.48 121 268.0001 Tm ( )Tj /TT5 1 Tf 12 0 0 12 124.7773 268.0001 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 131.9533 268.0001 Tm ( )Tj /TT6 1 Tf 12 0 0 12 135.7306 263.0001 Tm ( )Tj ET q 136 259 6 12 re W n BT /TT5 1 Tf 12 0 0 12 136 263 Tm <00a4>Tj ET Q q 136 271 6 12 re W n BT /TT5 1 Tf 12 0 0 12 136 270 Tm <00a3>Tj ET Q 142 271.875 m 153.25 271.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 143 274 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 155 263 Tm 0 Tc ( )Tj ET q 155 259 8 12 re W n BT /TT5 1 Tf 12 0 0 12 155 263 Tm <00a6>Tj ET Q q 155 271 8 12 re W n BT /TT5 1 Tf 12 0 0 12 155 270 Tm <00a5>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 161 278 Tm (2)Tj ET 168 271.875 m 202.25 271.875 l S BT 9.36 0 0 9.36 182 274 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 172.6919 263 Tm (3)Tj 9.36 0 0 9.36 177.4877 258 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 191.6608 263 Tm 0 Tc (2)Tj /TT5 1 Tf 9 0 0 9 196.4566 258 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 204 258 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.4167 TD <00a5>Tj ET q 204 262 8 13 re W n BT 12 0 0 12 204 266 Tm <00b4>Tj 0 -0.25 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 210 268.0001 Tm (u)Tj ET 210 278.875 m 216.25 278.875 l S 214 281 m 214.25 281 l 216.25 279 l 216.25 278.75 l 216 278.75 l 214 280.75 l f 216 279 m 216.25 279 l 216.25 278.75 l 214.25 276.75 l 214 276.75 l 214 277 l f BT 9.36 0 0 9.36 217 263 Tm (r)Tj ET 217 270.875 m 221.25 270.875 l S 219 273 m 219.25 273 l 221.25 271 l 221.25 270.75 l 221 270.75 l 219 272.75 l f 221 271 m 221.25 271 l 221.25 270.75 l 219.25 268.75 l 219 268.75 l 219 269 l f BT 12.48 0 0 12.48 222 268.0001 Tm ( )Tj /TT6 1 Tf 12 0 0 12 225.7773 268.0001 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 232.9533 268.0001 Tm ( )Tj /TT6 1 Tf 12 0 0 12 236.7306 258 Tm ( )Tj /TT5 1 Tf 0.0225 0 TD <00a4>Tj 0 1.4167 TD <00a3>Tj ET q 237 262 6 13 re W n BT 12 0 0 12 237 266 Tm <00b2>Tj 0 -0.25 TD <00b2>Tj ET Q 243 271.875 m 267.25 271.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 252 274 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 261.55 260 Tm 0 Tc <0065>Tj ET 270 271.875 m 286.25 271.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 271 274 Tm (d)Tj 7.28 0 0 7.28 277.3146 279 Tm (2)Tj 9.36 0 0 9.36 282.2254 274 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 280.2221 263 Tm 0 Tc (2)Tj 12.48 0 0 12.48 288 268.0001 Tm ( )Tj /TT5 1 Tf 12 0 0 12 291.7773 268.0001 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 298.9533 268.0001 Tm ( )Tj /TT6 1 Tf 12 0 0 12 302.7306 263.0001 Tm ( )Tj ET q 303 259 6 12 re W n BT /TT5 1 Tf 12 0 0 12 303 263 Tm <00a4>Tj ET Q q 303 271 6 12 re W n BT /TT5 1 Tf 12 0 0 12 303 270 Tm <00a3>Tj ET Q 309 271.875 m 320.25 271.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 310 274 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 322 263 Tm 0 Tc ( )Tj ET q 322 259 8 12 re W n BT /TT5 1 Tf 12 0 0 12 322 263 Tm <00a6>Tj ET Q q 322 271 8 12 re W n BT /TT5 1 Tf 12 0 0 12 322 270 Tm <00a5>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 328 278 Tm (2)Tj ET 335 271.875 m 369.25 271.875 l S BT 9.36 0 0 9.36 342 274 Tm 0.0202 Tc (cos)Tj /TT5 1 Tf 9 0 0 9 357.1326 274 Tm 0 Tc <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 336 258 Tm (r)Tj 7.28 0 0 7.28 339.692 263 Tm (3)Tj 9.36 0 0 9.36 344.4877 258 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 358.6608 263 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 363.4566 258 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 371 258 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj 0 1.4167 TD <00a5>Tj ET q 371 262 8 13 re W n BT 12 0 0 12 371 266 Tm <00b4>Tj 0 -0.25 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 377 268.0001 Tm (u)Tj ET 377 278.875 m 383.25 278.875 l S 381 281 m 381.25 281 l 383.25 279 l 383.25 278.75 l 383 278.75 l 381 280.75 l f 383 279 m 383.25 279 l 383.25 278.75 l 381.25 276.75 l 381 276.75 l 381 277 l f BT 9.36 0 0 9.36 384 263 Tm (r)Tj ET 384 270.875 m 388.25 270.875 l S 386 273 m 386.25 273 l 388.25 271 l 388.25 270.75 l 388 270.75 l 386 272.75 l f 388 271 m 388.25 271 l 388.25 270.75 l 386.25 268.75 l 386 268.75 l 386 269 l f BT /TT5 1 Tf 9 0 0 9 389 263 Tm <008c>Tj /TT4 1 Tf 12.48 0 0 12.48 90 225 Tm 0.0215 Tc 0.2149 Tw (So now we compute the cross product )Tj /TT5 1 Tf 12 0 0 12 333.4644 225 Tm 0 Tc 0 Tw <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 340.9213 225 Tm 0.0194 Tc 0.1937 Tw [( only the mixed terms matter )]TJ -21.5482 -1.2821 TD 0.024 Tc 0.2396 Tw (because parallel vectors have product )Tj /TT6 1 Tf 12 0 0 12 311.9883 209 Tm 0 Tc 0 Tw (=)Tj /TT4 1 Tf 12.48 0 0 12.48 319.3852 209 Tm 0.1027 Tc ( 0)Tj -18.3802 -2.0032 TD 0 Tc (a)Tj ET 90 194.875 m 96.25 194.875 l S 94 197 m 94.25 197 l 96.25 195 l 96.25 194.75 l 96 194.75 l 94 196.75 l f 96 195 m 96.25 195 l 96.25 194.75 l 94.25 192.75 l 94 192.75 l 94 193 l f BT 12.48 0 0 12.48 97 184 Tm ( )Tj /TT6 1 Tf 12 0 0 12 100.8603 184 Tm (�)Tj /TT4 1 Tf 12.48 0 0 12.48 108.1923 184 Tm 0.0881 Tc ( v)Tj ET 112 194.875 m 118.25 194.875 l S 116 197 m 116.25 197 l 118.25 195 l 118.25 194.75 l 118 194.75 l 116 196.75 l f 118 195 m 118.25 195 l 118.25 194.75 l 116.25 192.75 l 116 192.75 l 116 193 l f BT 12.48 0 0 12.48 119 184 Tm 0 Tc ( )Tj /TT6 1 Tf 12 0 0 12 122.7283 184 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 129.8103 184 Tm 0.0628 Tc ( u)Tj ET 134 194.875 m 140.25 194.875 l S 138 197 m 138.25 197 l 140.25 195 l 140.25 194.75 l 140 194.75 l 138 196.75 l f 140 195 m 140.25 195 l 140.25 194.75 l 138.25 192.75 l 138 192.75 l 138 193 l f BT 9.36 0 0 9.36 141 179 Tm 0 Tc (r)Tj ET 141 186.875 m 145.25 186.875 l S 143 189 m 143.25 189 l 145.25 187 l 145.25 186.75 l 145 186.75 l 143 188.75 l f 145 187 m 145.25 187 l 145.25 186.75 l 143.25 184.75 l 143 184.75 l 143 185 l f BT 12.48 0 0 12.48 146 184 Tm ( )Tj /TT6 1 Tf 12 0 0 12 149.7283 184 Tm (�)Tj /TT4 1 Tf 12.48 0 0 12.48 156.8103 184 Tm 0.0628 Tc ( u)Tj ET 161 194.875 m 167.25 194.875 l S 165 197 m 165.25 197 l 167.25 195 l 167.25 194.75 l 167 194.75 l 165 196.75 l f 167 195 m 167.25 195 l 167.25 194.75 l 165.25 192.75 l 165 192.75 l 165 193 l f BT 9.36 0 0 9.36 168 179 Tm 0 Tc (r)Tj ET 168 186.875 m 172.25 186.875 l S 170 189 m 170.25 189 l 172.25 187 l 172.25 186.75 l 172 186.75 l 170 188.75 l f 172 187 m 172.25 187 l 172.25 186.75 l 170.25 184.75 l 170 184.75 l 170 185 l f BT /TT5 1 Tf 9 0 0 9 173 179 Tm <008c>Tj ET 180 187.875 m 191.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 181 190 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 193 174 Tm 0 Tc ( )Tj ET q 193 170 6 17 re W n BT /TT5 1 Tf 12 0 0 12 193 171 Tm <0096>Tj ET Q BT /TT5 1 Tf 12 0 0 12 193 192 Tm <0095>Tj 0 -1.1667 TD <00b3>Tj 0 0.1667 TD <00b3>Tj ET q 193 174 6 18 re W n BT 12 0 0 12 193 168 Tm <00b3>Tj ET Q 199 187.875 m 223.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 208 190 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 217.55 176 Tm 0 Tc <0065>Tj /TT6 1 Tf 12 0 0 12 225 177 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a4>Tj ET q 225 187 6 14 re W n BT 12 0 0 12 225 188 Tm <00a3>Tj ET Q q 225 181 6 7 re W n BT 12 0 0 12 225 185 Tm <00b2>Tj 0 -0.75 TD <00b2>Tj ET Q 231 187.875 m 247.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 232 190 Tm (d)Tj 7.28 0 0 7.28 238.3146 195 Tm (2)Tj 9.36 0 0 9.36 243.2254 190 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 241.2221 179 Tm 0 Tc (2)Tj 12.48 0 0 12.48 249 184 Tm ( )Tj /TT5 1 Tf 12 0 0 12 252.7773 184 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 259.9533 184 Tm ( )Tj /TT6 1 Tf 12 0 0 12 263.7306 179 Tm ( )Tj ET q 264 175 6 12 re W n BT /TT5 1 Tf 12 0 0 12 264 179 Tm <00a4>Tj ET Q q 264 187 6 12 re W n BT /TT5 1 Tf 12 0 0 12 264 186 Tm <00a3>Tj ET Q 270 187.875 m 281.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 271 190 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 283 179 Tm 0 Tc ( )Tj ET q 283 175 8 12 re W n BT /TT5 1 Tf 12 0 0 12 283 179 Tm <00a6>Tj ET Q q 283 187 8 12 re W n BT /TT5 1 Tf 12 0 0 12 283 186 Tm <00a5>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 289 194 Tm (2)Tj ET 296 187.875 m 330.25 187.875 l S BT 9.36 0 0 9.36 310 190 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 300.692 179 Tm (3)Tj 9.36 0 0 9.36 305.4877 174 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 319.6608 179 Tm 0 Tc (2)Tj /TT5 1 Tf 9 0 0 9 324.4566 174 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 332 177 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 332 187 8 14 re W n BT 12 0 0 12 332 188 Tm <00a5>Tj ET Q q 332 181 8 7 re W n BT 12 0 0 12 332 185 Tm <00b4>Tj 0 -0.75 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 338 184 Tm ( )Tj /TT5 1 Tf 12 0 0 12 341.7773 184 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 348.9532 184 Tm ( )Tj /TT6 1 Tf 12 0 0 12 352.7306 177 Tm ( )Tj /TT5 1 Tf 0.0225 0 TD <00a4>Tj ET q 353 187 6 14 re W n BT 12 0 0 12 353 188 Tm <00a3>Tj ET Q q 353 181 6 7 re W n BT 12 0 0 12 353 185 Tm <00b2>Tj 0 -0.75 TD <00b2>Tj ET Q BT /TT6 1 Tf 12 0 0 12 358 177 Tm ( )Tj /TT5 1 Tf T* <00a4>Tj ET q 358 187 6 14 re W n BT 12 0 0 12 358 188 Tm <00a3>Tj ET Q q 358 181 6 7 re W n BT 12 0 0 12 358 185 Tm <00b2>Tj 0 -0.75 TD <00b2>Tj ET Q 364 187.875 m 388.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 373 190 Tm (1)Tj -0.8547 -1.4957 TD 0.0659 Tc (rsin)Tj /TT5 1 Tf 9 0 0 9 382.55 176 Tm 0 Tc <0065>Tj ET 391 187.875 m 407.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 392 190 Tm (d)Tj 7.28 0 0 7.28 398.3146 195 Tm (2)Tj 9.36 0 0 9.36 403.2253 190 Tm (r)Tj -1.1993 -1.7094 TD 0.0756 Tc (dt)Tj 7.28 0 0 7.28 401.2221 179 Tm 0 Tc (2)Tj /TT6 1 Tf 12 0 0 12 409 177 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 409 187 8 14 re W n BT 12 0 0 12 409 188 Tm <00a5>Tj ET Q q 409 181 8 7 re W n BT 12 0 0 12 409 185 Tm <00b4>Tj 0 -0.75 TD <00b4>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 415 184 Tm ( )Tj /TT5 1 Tf 12 0 0 12 418.7773 184 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 425.9533 184 Tm ( )Tj /TT6 1 Tf 12 0 0 12 429.7306 179 Tm ( )Tj ET q 430 175 6 12 re W n BT /TT5 1 Tf 12 0 0 12 430 179 Tm <00a4>Tj ET Q q 430 187 6 12 re W n BT /TT5 1 Tf 12 0 0 12 430 186 Tm <00a3>Tj ET Q 436 187.875 m 447.25 187.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 437 190 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 449 179 Tm 0 Tc ( )Tj ET q 449 175 8 12 re W n BT /TT5 1 Tf 12 0 0 12 449 179 Tm <00a6>Tj ET Q q 449 187 8 12 re W n BT /TT5 1 Tf 12 0 0 12 449 186 Tm <00a5>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 455 194 Tm (2)Tj ET 462 187.875 m 496.25 187.875 l S BT 9.36 0 0 9.36 469 190 Tm 0.0202 Tc (cos)Tj /TT5 1 Tf 9 0 0 9 484.1326 190 Tm 0 Tc <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 463 174 Tm (r)Tj 7.28 0 0 7.28 466.692 179 Tm (3)Tj 9.36 0 0 9.36 471.4877 174 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 485.6608 179 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 490.4566 174 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 498 177 Tm ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 498 187 8 14 re W n BT 12 0 0 12 498 188 Tm <00a5>Tj ET Q q 498 181 8 7 re W n BT 12 0 0 12 498 185 Tm <00b4>Tj 0 -0.75 TD <00b4>Tj ET Q BT /TT6 1 Tf 12 0 0 12 504 174 Tm ( )Tj ET q 504 170 6 17 re W n BT /TT5 1 Tf 12 0 0 12 504 171 Tm <0098>Tj ET Q BT /TT5 1 Tf 12 0 0 12 504 192 Tm <0097>Tj 0 -1.1667 TD <00b5>Tj 0 0.1667 TD <00b5>Tj ET q 504 174 6 18 re W n BT 12 0 0 12 504 168 Tm <00b5>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 90 157 Tm 0.0225 Tc 0.2255 Tw (We can cancel the second derivative terms)Tj /TT6 1 Tf 12 0 0 12 90 130 Tm 0 Tc 0 Tw (=)Tj /TT4 1 Tf 12.48 0 0 12.48 96.9769 130 Tm 0.0495 Tc ( u)Tj ET 101 140.875 m 107.25 140.875 l S 105 143 m 105.25 143 l 107.25 141 l 107.25 140.75 l 107 140.75 l 105 142.75 l f 107 141 m 107.25 141 l 107.25 140.75 l 105.25 138.75 l 105 138.75 l 105 139 l f BT 9.36 0 0 9.36 108 125 Tm 0 Tc (r)Tj ET 108 132.875 m 112.25 132.875 l S 110 135 m 110.25 135 l 112.25 133 l 112.25 132.75 l 112 132.75 l 110 134.75 l f 112 133 m 112.25 133 l 112.25 132.75 l 110.25 130.75 l 110 130.75 l 110 131 l f BT 12.48 0 0 12.48 113 130 Tm ( )Tj /TT6 1 Tf 12 0 0 12 116.7283 130 Tm (�)Tj /TT4 1 Tf 12.48 0 0 12.48 123.8103 130 Tm 0.0628 Tc ( u)Tj ET 128 140.875 m 134.25 140.875 l S 132 143 m 132.25 143 l 134.25 141 l 134.25 140.75 l 134 140.75 l 132 142.75 l f 134 141 m 134.25 141 l 134.25 140.75 l 132.25 138.75 l 132 138.75 l 132 139 l f BT 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12 177 136 Tm <0095>Tj 0 -1 TD <00b3>Tj 0 0 TD <00b3>Tj ET q 177 120 6 16 re W n BT 12 0 0 12 177 112 Tm <00b3>Tj ET Q BT /TT4 1 Tf 12.48 0 0 12.48 182 130 Tm -0.0554 Tc ( )Tj /TT5 1 Tf 12 0 0 12 191.995 130 Tm 0 Tc <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 197.139 130 Tm -0.1107 Tc ( )Tj ET 198 133.875 m 232.25 133.875 l S BT 9.36 0 0 9.36 212 136 Tm 0 Tc (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 202.6919 125 Tm (4)Tj 9.36 0 0 9.36 207.4877 120 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 221.6608 125 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 226.4566 120 Tm <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 234 130 Tm ( )Tj /TT6 1 Tf 12 0 0 12 237.1783 130 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 243.2153 130 Tm -0.0421 Tc ( )Tj ET 250 133.875 m 284.25 133.875 l S BT 9.36 0 0 9.36 257 136 Tm 0.0202 Tc (cos)Tj /TT5 1 Tf 9 0 0 9 272.1326 136 Tm 0 Tc <0065>Tj /TT4 1 Tf 9.36 0 0 9.36 251 120 Tm (r)Tj 7.28 0 0 7.28 254.692 125 Tm (3)Tj 9.36 0 0 9.36 259.4877 120 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 273.6608 125 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 278.4566 120 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 286 120 Tm ( )Tj ET q 286 116 6 16 re W n BT /TT5 1 Tf 12 0 0 12 286 117 Tm <0098>Tj ET Q BT /TT5 1 Tf 12 0 0 12 286 136 Tm <0097>Tj 0 -1 TD <00b5>Tj 0 0 TD <00b5>Tj ET q 286 120 6 16 re W n BT 12 0 0 12 286 112 Tm <00b5>Tj ET Q BT /TT6 1 Tf 12 0 0 12 90 92 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 96.9769 92 Tm 0.0495 Tc ( u)Tj ET 101 102.875 m 107.25 102.875 l S 105 105 m 105.25 105 l 107.25 103 l 107.25 102.75 l 107 102.75 l 105 104.75 l f 107 103 m 107.25 103 l 107.25 102.75 l 105.25 100.75 l 105 100.75 l 105 101 l f BT 9.36 0 0 9.36 108 87 Tm 0 Tc (r)Tj ET 108 94.875 m 112.25 94.875 l S 110 97 m 110.25 97 l 112.25 95 l 112.25 94.75 l 112 94.75 l 110 96.75 l f 112 95 m 112.25 95 l 112.25 94.75 l 110.25 92.75 l 110 92.75 l 110 93 l f BT 12.48 0 0 12.48 113 92 Tm ( )Tj /TT6 1 Tf 12 0 0 12 116.7283 92 Tm (�)Tj /TT4 1 Tf 12.48 0 0 12.48 123.8103 92 Tm 0.0628 Tc ( u)Tj ET 128 102.875 m 134.25 102.875 l S 132 105 m 132.25 105 l 134.25 103 l 134.25 102.75 l 134 102.75 l 132 104.75 l f 134 103 m 134.25 103 l 134.25 102.75 l 132.25 100.75 l 132 100.75 l 132 101 l f BT 9.36 0 0 9.36 135 87 Tm 0 Tc (r)Tj ET 135 94.875 m 139.25 94.875 l S 137 97 m 137.25 97 l 139.25 95 l 139.25 94.75 l 139 94.75 l 137 96.75 l f 139 95 m 139.25 95 l 139.25 94.75 l 137.25 92.75 l 137 92.75 l 137 93 l f BT /TT5 1 Tf 9 0 0 9 140 87 Tm <008c>Tj /TT6 1 Tf 12 0 0 12 145.9748 84 Tm ( )Tj /TT5 1 Tf 0.0021 0 TD <00a4>Tj ET q 146 95 6 15 re W n BT 12 0 0 12 146 97 Tm <00a3>Tj ET Q q 146 88 6 9 re W n BT 12 0 0 12 146 92 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q 152 95.875 m 163.25 95.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 153 98 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 165 84 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 165 95 8 15 re W n BT 12 0 0 12 165 97 Tm <00a5>Tj ET Q q 165 88 8 9 re W n BT 12 0 0 12 165 92 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 171 105 Tm (3)Tj /TT6 1 Tf 12 0 0 12 176.7106 82 Tm ( )Tj ET q 177 78 6 16 re W n BT /TT5 1 Tf 12 0 0 12 177 79 Tm <0096>Tj ET Q BT /TT5 1 Tf 12 0 0 12 177 98 Tm <0095>Tj 0 -1 TD <00b3>Tj 0 0 TD <00b3>Tj ET q 177 82 6 16 re W n BT 12 0 0 12 177 74 Tm <00b3>Tj ET Q BT /TT6 1 Tf 12 0 0 12 182 87 Tm ( )Tj ET q 182 83 6 12 re W n BT /TT5 1 Tf 12 0 0 12 182 87 Tm <00a4>Tj ET Q q 182 95 6 12 re W n BT /TT5 1 Tf 12 0 0 12 182 94 Tm <00a3>Tj ET Q BT /TT5 1 Tf 12 0 0 12 187 92 Tm <003c>Tj ET 195 95.875 m 202.25 95.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 196 98 Tm (1)Tj 0 -1.4957 TD (r)Tj 12.48 0 0 12.48 204 92 Tm ( )Tj /TT6 1 Tf 12 0 0 12 207.7803 92 Tm (+)Tj /TT4 1 Tf 12.48 0 0 12.48 214.9613 92 Tm 0.0119 Tc 0.1182 Tw [( cos)]TJ /TT5 1 Tf 12 0 0 12 239.9174 92 Tm 0 Tc 0 Tw <0065>Tj /TT6 1 Tf 0.5681 -0.4167 TD ( )Tj ET q 247 83 8 12 re W n BT /TT5 1 Tf 12 0 0 12 247 87 Tm <00a6>Tj ET Q q 247 95 8 12 re W n BT /TT5 1 Tf 12 0 0 12 247 94 Tm <00a5>Tj ET Q 254 95.875 m 288.25 95.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 268 98 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 258.692 87 Tm (3)Tj 9.36 0 0 9.36 263.4877 82 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 277.6608 87 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 282.4566 82 Tm <0065>Tj /TT6 1 Tf 12 0 0 12 290 82 Tm ( )Tj ET q 290 78 6 16 re W n BT /TT5 1 Tf 12 0 0 12 290 79 Tm <0098>Tj ET Q BT /TT5 1 Tf 12 0 0 12 290 98 Tm <0097>Tj 0 -1 TD <00b5>Tj 0 0 TD <00b5>Tj ET q 290 82 6 16 re W n BT 12 0 0 12 290 74 Tm <00b5>Tj ET Q endstream endobj 3 0 obj << /ProcSet [/PDF /Text ] /Font << /TT4 4 0 R /TT5 5 0 R /TT6 6 0 R >> /ExtGState << /GS1 7 0 R >> >> endobj 10 0 obj << /Length 6110 >> stream BT /TT4 1 Tf 12.48 0 0 12.48 90 709 Tm 0 g /GS1 gs 0.0277 Tc 0.2777 Tw (Since r)Tj /TT6 1 Tf 12 0 0 12 134.7286 709 Tm 0 Tc 0 Tw (\()Tj /TT4 1 Tf 12.48 0 0 12.48 139.3307 709 Tm 0.0106 Tc (1 )Tj /TT6 1 Tf 12 0 0 12 151.3178 709 Tm 0 Tc (+)Tj /TT4 1 Tf 12.48 0 0 12.48 158.9027 709 Tm 0.0128 Tc 0.1281 Tw [( cos )]TJ /TT5 1 Tf 12 0 0 12 189.2562 709 Tm 0 Tc 0 Tw <0065>Tj /TT6 1 Tf 0.5857 0 TD (\))Tj /TT4 1 Tf 12.48 0 0 12.48 201.0582 709 Tm ( )Tj /TT6 1 Tf 12 0 0 12 205.0516 709 Tm (=)Tj /TT4 1 Tf 12.48 0 0 12.48 212.6365 709 Tm 0.0159 Tc 0.1592 Tw [( 1, we may solve for the left 1 to get 1 )]TJ /TT6 1 Tf 12 0 0 12 455.5079 709 Tm 0 Tc 0 Tw (=)Tj /TT4 1 Tf 12.48 0 0 12.48 463.0928 709 Tm ( )Tj ET 0 G 0 J 0 j 0.25 w 10 M []0 d 1 i 468 712.875 m 475.25 712.875 l S BT 9.36 0 0 9.36 469 715 Tm (1)Tj 0 -1.4957 TD (r)Tj 12.48 0 0 12.48 477 709 Tm ( )Tj /TT5 1 Tf 12 0 0 12 480.8453 709 Tm <003c>Tj /TT4 1 Tf 12.48 0 0 12.48 488.1493 709 Tm 0.0092 Tc 0.0921 Tw [( cos )]TJ /TT5 1 Tf 12 0 0 12 517.3777 709 Tm 0 Tc 0 Tw <0065>Tj /TT4 1 Tf 12.48 0 0 12.48 524.3116 709 Tm 0.0055 Tc (, )Tj -36.2429 -2.6442 TD 0.0072 Tc (so )Tj /TT6 1 Tf 12 0 0 12 89.8181 676 Tm 0 Tc (=)Tj /TT4 1 Tf 12.48 0 0 12.48 96.8671 676 Tm 0.0586 Tc ( u)Tj ET 101 686.875 m 107.25 686.875 l S 105 689 m 105.25 689 l 107.25 687 l 107.25 686.75 l 107 686.75 l 105 688.75 l f 107 687 m 107.25 687 l 107.25 686.75 l 105.25 684.75 l 105 684.75 l 105 685 l f 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BT 12 0 0 12 146 676 Tm <00b2>Tj 0 -0.5833 TD <00b2>Tj ET Q 152 679.875 m 163.25 679.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 153 682 Tm 0.1797 Tc (dr)Tj 0 -1.4957 TD 0.1278 Tc (dt)Tj /TT6 1 Tf 12 0 0 12 165 668 Tm 0 Tc ( )Tj /TT5 1 Tf 0 0 TD <00a6>Tj ET q 165 679 8 15 re W n BT 12 0 0 12 165 681 Tm <00a5>Tj ET Q q 165 672 8 9 re W n BT 12 0 0 12 165 676 Tm <00b4>Tj 0 -0.5833 TD <00b4>Tj ET Q BT /TT4 1 Tf 9.36 0 0 9.36 171 689 Tm (3)Tj /TT6 1 Tf 12 0 0 12 176.7106 666 Tm ( )Tj ET q 177 662 6 16 re W n BT /TT5 1 Tf 12 0 0 12 177 663 Tm <0096>Tj ET Q BT /TT5 1 Tf 12 0 0 12 177 682 Tm <0095>Tj 0 -1 TD <00b3>Tj 0 0 TD <00b3>Tj ET q 177 666 6 16 re W n BT 12 0 0 12 177 658 Tm <00b3>Tj ET Q BT 12 0 0 12 182 676 Tm <003c>Tj ET 190 679.875 m 224.25 679.875 l S BT /TT4 1 Tf 9.36 0 0 9.36 204 682 Tm (1)Tj -1.3889 -1.7094 TD (r)Tj 7.28 0 0 7.28 194.692 671.0001 Tm (3)Tj 9.36 0 0 9.36 199.4877 666 Tm 0.0786 Tc (sin)Tj 7.28 0 0 7.28 213.6608 671.0001 Tm 0 Tc (3)Tj /TT5 1 Tf 9 0 0 9 218.4566 666 Tm 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