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Waluigi function

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Apr 23rd, 2019
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  1. x(t) = ((-3/10 sin(17/11 - 10 t) - 54/17 sin(59/38 - 9 t) - 241/34 sin(36/23 - 8 t) - 858/73 sin(36/23 - 5 t) - 487/35 sin(36/23 - 4 t) - 542/27 sin(11/7 - 2 t) + 181/22 sin(t + 91/58) + 41/30 sin(3 t + 25/16) + 20/21 sin(6 t + 27/17) + 149/30 sin(7 t + 49/31) + 26/29 sin(11 t + 61/13) + 1/5 sin(12 t + 177/38) + 1133/15) θ(87 π - t) θ(t - 83 π) + (-1/120 sin(4/17 - 26 t) - 6/19 sin(92/61 - 25 t) - 4/31 sin(35/29 - 24 t) - 9/46 sin(25/16 - 23 t) - 7/8 sin(49/32 - 17 t) - 17/15 sin(58/39 - 16 t) - 92/123 sin(61/39 - 13 t) - 2049/40 sin(47/30 - 3 t) - 495/26 sin(39/25 - 2 t) + 472/39 sin(t + 47/30) + 982/25 sin(4 t + 41/26) + 341/57 sin(5 t + 45/28) + 189/20 sin(6 t + 19/12) + 81/58 sin(7 t + 39/25) + 55/21 sin(8 t + 52/33) + 229/39 sin(9 t + 67/42) + 205/33 sin(10 t + 59/37) + 23/28 sin(11 t + 47/10) + 9/7 sin(12 t + 48/31) + 57/26 sin(14 t + 67/42) + 13/37 sin(15 t + 167/36) + 27/28 sin(18 t + 8/5) + 23/19 sin(19 t + 64/39) + 70/33 sin(20 t + 21/13) + 3/23 sin(21 t + 62/37) + 29/57 sin(22 t + 49/31) + 1/35 sin(27 t + 218/51) + 48/55 sin(28 t + 47/29) + 2/25 sin(29 t + 47/28) + 3/43 sin(30 t + 29/20) + 1/25 sin(31 t + 137/31) + 963/20) θ(83 π - t) θ(t - 79 π) + (-6/35 sin(69/44 - t) + 4/43 sin(2 t + 193/41) + 19/34 sin(3 t + 96/61) + 1/48 sin(4 t + 35/22) + 2/31 sin(5 t + 30/19) + 1/9 sin(6 t + 49/31) + 1/11 sin(7 t + 49/31) + 1/463 sin(8 t + 214/47) + 1/15 sin(9 t + 49/31) + 1/25 sin(10 t + 35/22) + 1/58 sin(11 t + 35/22) + 1/60 sin(12 t + 65/41) + 997/12) θ(79 π - t) θ(t - 75 π) + (-15/32 sin(38/25 - 12 t) - 30/47 sin(61/41 - 11 t) - sin(87/56 - 7 t) - 294/13 sin(47/30 - 3 t) - 60/23 sin(14/9 - 2 t) + 285/43 sin(t + 47/30) + 256/61 sin(4 t + 73/47) + 52/33 sin(5 t + 179/38) + 29/43 sin(6 t + 69/43) + 19/10 sin(8 t + 58/37) + 2/37 sin(9 t + 142/61) + 1/46 sin(10 t + 81/40) + 17685/217) θ(75 π - t) θ(t - 71 π) + (-64/25 sin(58/37 - 4 t) - 67/40 sin(47/30 - 3 t) + 33/35 sin(t + 11/7) + 11/25 sin(2 t + 52/33) + 10/7 sin(5 t + 74/47) + 1/11 sin(6 t + 14/3) + 13/17 sin(7 t + 85/54) + 35/106 sin(8 t + 146/31) + 17/45 sin(9 t + 30/19) + 7/33 sin(10 t + 27/17) + 2/15 sin(11 t + 43/27) + 2/31 sin(12 t + 108/23) - 4135/149) θ(71 π - t) θ(t - 67 π) + (-11/35 sin(88/61 - 12 t) - 35/29 sin(44/29 - 11 t) - 33/34 sin(48/31 - 8 t) - 31/21 sin(173/115 - 7 t) - 16/15 sin(61/39 - 6 t) - 10/19 sin(24/17 - t) + 98/27 sin(2 t + 247/53) + 565/12 sin(3 t + 27/17) + 37/15 sin(4 t + 37/22) + 6/41 sin(5 t + 28/31) + 55/17 sin(9 t + 31/19) + 23/16 sin(10 t + 57/35) - 687/29) θ(67 π - t) θ(t - 63 π) + (-170/39 sin(47/30 - t) + 881/19 sin(2 t + 11/7) + 191/42 sin(3 t + 74/47) + 1/23 sin(4 t + 98/29) + 51/26 sin(5 t + 103/22) + 257/129 sin(6 t + 19/12) + 34/27 sin(7 t + 46/29) + 40/29 sin(8 t + 46/29) + 34/37 sin(9 t + 108/23) + 8/65 sin(10 t + 43/24) + 38/31 sin(11 t + 35/22) + 37/49 sin(12 t + 29/18) + 3799/41) θ(63 π - t) θ(t - 59 π) + (-70/33 sin(25/16 - 10 t) - 15/44 sin(65/42 - 9 t) - 177/29 sin(11/7 - 6 t) - 23/38 sin(47/30 - 5 t) - 1261/23 sin(11/7 - 2 t) + 20/9 sin(t + 136/29) + 18/19 sin(3 t + 43/27) + 1/37 sin(4 t + 83/32) + 3/11 sin(7 t + 39/25) + 1/34 sin(8 t + 229/51) + 11/25 sin(11 t + 27/17) + 1/34 sin(12 t + 47/28) + 4221/20) θ(59 π - t) θ(t - 55 π) + (731/79 sin(t + 19/12) + 2597/45 sin(2 t + 52/33) + 119/25 sin(3 t + 212/45) + 21/29 sin(4 t + 151/101) + 50/23 sin(5 t + 133/83) + 196/39 sin(6 t + 49/31) + 92/79 sin(7 t + 61/13) + 27/29 sin(8 t + 11/7) + 29/35 sin(9 t + 29/18) + 46/43 sin(10 t + 62/39) + 12/31 sin(11 t + 47/10) + 37/30 sin(12 t + 8/5) - 486/19) θ(55 π - t) θ(t - 51 π) + (-37/38 sin(35/23 - 22 t) - 14/11 sin(36/23 - 19 t) - 47/19 sin(29/19 - 11 t) - 45/17 sin(29/19 - 10 t) - 685/46 sin(54/35 - 8 t) - 727/57 sin(17/11 - 6 t) - 175/4 sin(39/25 - 3 t) - 1228/43 sin(64/41 - 2 t) + 2162/21 sin(t + 96/61) + 184/17 sin(4 t + 47/30) + 241/31 sin(5 t + 45/29) + 209/25 sin(7 t + 73/47) + 62/11 sin(9 t + 59/38) + 11/19 sin(12 t + 80/17) + 10/23 sin(13 t + 77/17) + 55/16 sin(14 t + 41/25) + 212/77 sin(15 t + 167/100) + 81/52 sin(16 t + 67/40) + 63/95 sin(17 t + 50/11) + 25/29 sin(18 t + 49/29) + 17/26 sin(20 t + 83/51) + 2/29 sin(21 t + 107/57) + 61/46 sin(23 t + 50/31) + 23/42 sin(24 t + 75/16) + 2147/33) θ(51 π - t) θ(t - 47 π) + (-13/37 sin(32/21 - 11 t) - 311/47 sin(82/53 - 5 t) - 547/39 sin(25/16 - t) + 6/35 sin(2 t + 50/29) + 271/27 sin(3 t + 59/37) + 79/16 sin(4 t + 51/32) + 61/62 sin(6 t + 29/19) + 149/64 sin(7 t + 50/31) + 7/39 sin(8 t + 235/56) + 77/40 sin(9 t + 60/37) + 5/14 sin(10 t + 38/23) + 11/31 sin(12 t + 37/23) + 16/37 sin(13 t + 102/61) + 13/28 sin(14 t + 26/15) + 20/33 sin(15 t + 67/40) + 3/25 sin(16 t + 146/31) + 5/16 sin(17 t + 31/19) + 11/40 sin(18 t + 65/38) + 3/43 sin(19 t + 53/24) + 281/30) θ(47 π - t) θ(t - 43 π) + (-5/23 sin(37/25 - 38 t) - 15/22 sin(39/25 - 26 t) - 124/53 sin(199/133 - 14 t) - 49/23 sin(20/13 - 9 t) - 479/18 sin(58/37 - 5 t) + 1104/25 sin(t + 47/30) + 402/23 sin(2 t + 36/23) + 907/14 sin(3 t + 212/45) + 1213/20 sin(4 t + 96/61) + 463/17 sin(6 t + 39/25) + 1359/28 sin(7 t + 53/34) + 6412/171 sin(8 t + 53/34) + 652/43 sin(10 t + 202/43) + 35/24 sin(11 t + 147/32) + 265/41 sin(12 t + 53/34) + 196/89 sin(13 t + 61/41) + 62/27 sin(15 t + 53/35) + 100/41 sin(16 t + 52/33) + 34/39 sin(17 t + 169/36) + 3/26 sin(18 t + 199/43) + 37/14 sin(19 t + 54/35) + 85/29 sin(20 t + 23/15) + 152/37 sin(21 t + 43/28) + 29/11 sin(22 t + 43/28) + 39/28 sin(23 t + 53/34) + 24/47 sin(24 t + 83/18) + 69/53 sin(25 t + 164/35) + 58/57 sin(27 t + 80/53) + 7/31 sin(28 t + 24/19) + 2/33 sin(29 t + 41/27) + 9/26 sin(30 t + 93/20) + 3/20 sin(31 t + 97/49) + 7/25 sin(32 t + 169/36) + 10/11 sin(33 t + 49/32) + 13/18 sin(34 t + 67/46) + 11/8 sin(35 t + 67/44) + 19/21 sin(36 t + 61/40) + 5/19 sin(37 t + 35/24) + 1/29 sin(39 t + 99/34) - 116/17) θ(43 π - t) θ(t - 39 π) + (-12/31 sin(49/32 - 24 t) - 27/13 sin(26/17 - 19 t) - 158/159 sin(33/23 - 18 t) - 54/25 sin(37/25 - 17 t) - 73/31 sin(274/183 - 15 t) - 33/5 sin(58/39 - 14 t) - 241/23 sin(38/25 - 13 t) - 58/23 sin(32/21 - 11 t) - 210/41 sin(35/23 - 10 t) - 51/31 sin(85/57 - 9 t) - 46/33 sin(65/42 - 8 t) - 2627/73 sin(14/9 - 5 t) - 1718/39 sin(25/16 - 3 t) - 617/28 sin(14/9 - 2 t) + 244/9 sin(t + 52/33) + 627/26 sin(4 t + 52/33) + 243/26 sin(6 t + 11/7) + 247/30 sin(7 t + 8/5) + 43/24 sin(12 t + 47/31) + 21/43 sin(16 t + 37/27) + 15/13 sin(20 t + 49/31) + 1/7 sin(21 t + 514/147) + 133/40 sin(22 t + 51/31) + 1/8 sin(23 t + 73/29) + 31/37 sin(25 t + 49/29) - 4136/31) θ(39 π - t) θ(t - 35 π) + (-61/46 sin(49/32 - 22 t) - 15/8 sin(55/36 - 18 t) - 353/42 sin(59/38 - 13 t) - 703/10 sin(69/44 - t) + 891/31 sin(2 t + 63/40) + 53/20 sin(3 t + 39/25) + 61/35 sin(4 t + 27/17) + 43/23 sin(5 t + 131/28) + 1/11 sin(6 t + 59/13) + 34/7 sin(7 t + 68/43) + 50/29 sin(8 t + 69/43) + 199/31 sin(9 t + 35/22) + 481/43 sin(10 t + 19/12) + 192/19 sin(11 t + 46/29) + 44/27 sin(12 t + 125/78) + 3/40 sin(14 t + 61/25) + 3/2 sin(15 t + 65/41) + 23/29 sin(16 t + 80/51) + 2/3 sin(17 t + 29/18) + 5/31 sin(19 t + 23/16) + 37/112 sin(20 t + 19/12) + 67/52 sin(21 t + 21/13) + 2/5 sin(23 t + 49/30) + 2/25 sin(24 t + 54/37) + 11/30 sin(25 t + 53/33) + 12976/39) θ(35 π - t) θ(t - 31 π) + (-208/83 sin(43/28 - 15 t) - 33/53 sin(43/28 - 14 t) - 205/19 sin(48/31 - 9 t) - 169/46 sin(14/9 - 8 t) - 80/19 sin(69/44 - 6 t) - 425/49 sin(36/23 - 4 t) - 144/17 sin(47/30 - 2 t) - 439/23 sin(47/30 - t) + 37/13 sin(3 t + 80/51) + 73/27 sin(5 t + 36/23) + 479/44 sin(7 t + 19/12) + 4/9 sin(10 t + 59/37) + 137/26 sin(11 t + 43/27) + 29/28 sin(12 t + 155/33) + 50/27 sin(13 t + 46/29) + 10/23 sin(16 t + 50/31) + 8/7 sin(17 t + 61/38) + 19/66 sin(18 t + 136/29) + 37/39 sin(19 t + 37/23) + 4/25 sin(20 t + 117/25) - 2171/36) θ(31 π - t) θ(t - 27 π) + (-4/33 sin(17/16 - 20 t) - 23/35 sin(25/16 - 16 t) - 355/49 sin(47/30 - 11 t) - 253/25 sin(47/30 - 8 t) - 523/12 sin(69/44 - 4 t) + 641/11 sin(t + 113/24) + 7553/58 sin(2 t + 179/38) + 198/29 sin(3 t + 51/32) + 1119/73 sin(5 t + 52/33) + 33/13 sin(6 t + 61/13) + 115/28 sin(7 t + 174/37) + 191/9 sin(9 t + 47/30) + 433/54 sin(10 t + 47/30) + 107/35 sin(12 t + 47/10) + 157/18 sin(13 t + 11/7) + 43/14 sin(14 t + 14/9) + 24/31 sin(15 t + 67/45) + 172/57 sin(17 t + 19/12) + 14/51 sin(18 t + 45/28) + 81/32 sin(19 t + 14/9) + 9613/33) θ(27 π - t) θ(t - 23 π) + (-1/11 sin(14/9 - 19 t) - 83/43 sin(69/44 - 4 t) - 430/57 sin(102/65 - 3 t) + 91/20 sin(t + 245/52) + 177/31 sin(2 t + 11/7) + 26/61 sin(5 t + 108/23) + 28/29 sin(6 t + 74/47) + 5/7 sin(7 t + 47/30) + 51/31 sin(8 t + 74/47) + 31/27 sin(9 t + 41/26) + 35/52 sin(10 t + 19/12) + 1/110 sin(11 t + 82/23) + 17/52 sin(12 t + 43/27) + 13/41 sin(13 t + 149/93) + 34/57 sin(14 t + 84/53) + 9/38 sin(15 t + 43/27) + 8/47 sin(16 t + 53/33) + 2/11 sin(17 t + 91/57) + 1/9 sin(18 t + 67/42) - 11360/99) θ(23 π - t) θ(t - 19 π) + (-11/38 sin(38/25 - 20 t) - 10/27 sin(31/20 - 19 t) - 19/26 sin(37/24 - 17 t) - 13/12 sin(20/13 - 12 t) - 101/21 sin(17/11 - 10 t) - 85/22 sin(14/9 - 9 t) - 294/71 sin(45/29 - 8 t) - 271/25 sin(81/52 - 7 t) - 290/19 sin(53/34 - 5 t) - 1066/23 sin(36/23 - 2 t) - 101/5 sin(91/58 - t) + 61/10 sin(3 t + 65/41) + 908/25 sin(4 t + 30/19) + 127/22 sin(6 t + 68/43) + 93/20 sin(11 t + 99/62) + 26/27 sin(13 t + 53/33) + 13/66 sin(14 t + 47/31) + 14/33 sin(15 t + 48/29) + 25/19 sin(16 t + 139/87) + 23/19 sin(18 t + 123/77) - 6074/35) θ(19 π - t) θ(t - 15 π) + (-10/27 sin(43/29 - 14 t) + 285/32 sin(t + 14/9) + 2701/27 sin(2 t + 80/51) + 1303/22 sin(3 t + 245/52) + 525/26 sin(4 t + 25/16) + 526/11 sin(5 t + 36/23) + 191/13 sin(6 t + 53/34) + 162/23 sin(7 t + 179/38) + 323/29 sin(8 t + 108/23) + 105/16 sin(9 t + 136/29) + 281/30 sin(10 t + 47/10) + 119/26 sin(11 t + 47/30) + 281/51 sin(12 t + 53/34) + 17/7 sin(13 t + 14/9) + 75/31 sin(15 t + 25/16) + 68/39 sin(16 t + 14/9) + 5/13 sin(17 t + 19/13) + 64/29 sin(18 t + 47/30) + 12/17 sin(19 t + 67/43) + 11/23 sin(20 t + 32/21) - 6832/31) θ(15 π - t) θ(t - 11 π) + (-61/40 sin(64/41 - 39 t) - 19/17 sin(154/103 - 38 t) - 107/31 sin(58/37 - 24 t) - 48/7 sin(45/29 - 22 t) - 132/19 sin(69/44 - 21 t) - 37/14 sin(82/53 - 20 t) - 107/31 sin(53/34 - 18 t) - 1021/44 sin(102/65 - 16 t) - 4/9 sin(19/16 - 14 t) - 5/27 sin(92/91 - 12 t) - 227/18 sin(25/16 - 11 t) - 1117/33 sin(91/58 - 7 t) - 1490/29 sin(36/23 - 5 t) - 419/26 sin(39/25 - 4 t) + 5191/22 sin(t + 69/44) + 5012/61 sin(2 t + 146/31) + 3813/28 sin(3 t + 212/45) + 896/45 sin(6 t + 146/31) + 789/28 sin(8 t + 47/30) + 1832/75 sin(9 t + 39/25) + 677/24 sin(10 t + 80/17) + 65/16 sin(13 t + 144/31) + 358/31 sin(15 t + 193/41) + 137/36 sin(17 t + 71/46) + 91/32 sin(19 t + 14/9) + 38/15 sin(23 t + 131/28) + 157/35 sin(25 t + 48/31) + 22/21 sin(26 t + 89/19) + 69/35 sin(27 t + 36/23) + 31/56 sin(28 t + 29/20) + 47/29 sin(29 t + 133/29) + 5/33 sin(30 t + 73/16) + 62/19 sin(31 t + 35/22) + 64/33 sin(32 t + 215/46) + 2/29 sin(33 t + 80/47) + 4/25 sin(34 t + 109/24) + 32/19 sin(35 t + 38/25) + 40/31 sin(36 t + 41/26) + 23/34 sin(37 t + 164/35) + 121/97 sin(40 t + 202/43) + 437/12) θ(11 π - t) θ(t - 7 π) + (-1/2 sin(45/29 - 12 t) - 119/38 sin(39/25 - 11 t) - 165/26 sin(36/23 - 7 t) - 8281/460 sin(25/16 - 3 t) - 1389/10 sin(69/44 - 2 t) + 1493/41 sin(t + 69/44) + 23/29 sin(4 t + 49/32) + 59/25 sin(5 t + 245/52) + 79/29 sin(6 t + 127/27) + 35/23 sin(8 t + 64/41) + 101/29 sin(9 t + 80/17) + 139/70 sin(10 t + 58/37) + 10497/35) θ(7 π - t) θ(t - 3 π) + (-37/48 sin(91/58 - 9 t) - 1263/85 sin(36/23 - 6 t) - 2798/33 sin(69/44 - t) + 142/35 sin(2 t + 27/17) + 2885/43 sin(3 t + 63/40) + 446/31 sin(4 t + 179/38) + 331/34 sin(5 t + 80/51) + 49/24 sin(7 t + 48/31) + 15/41 sin(8 t + 8/5) + 100/41 sin(10 t + 43/27) + 71/22 sin(11 t + 19/12) + 3/19 sin(12 t + 26/15) - 5170/21) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2)))) y(t) = ((-219/58 sin(39/25 - 9 t) - 221/33 sin(47/30 - 6 t) - 275/21 sin(36/23 - 5 t) + 243/14 sin(t + 11/7) + 1881/37 sin(2 t + 11/7) + 70/51 sin(3 t + 41/25) + 1959/83 sin(4 t + 11/7) + 198/31 sin(7 t + 41/26) + 127/27 sin(8 t + 46/29) + 17/28 sin(10 t + 82/55) + 22/87 sin(11 t + 164/35) + 46/27 sin(12 t + 19/12) - 23915/118) θ(87 π - t) θ(t - 83 π) + (-12/35 sin(43/28 - 27 t) - 57/34 sin(173/115 - 23 t) - 27/14 sin(100/67 - 22 t) - 55/28 sin(23/15 - 21 t) - 22/51 sin(167/111 - 17 t) - 19/20 sin(20/13 - 12 t) - 884/33 sin(36/23 - 3 t) - 134/39 sin(47/30 - t) + 158/23 sin(2 t + 58/37) + 240/31 sin(4 t + 41/26) + 199/19 sin(5 t + 19/12) + 41/16 sin(6 t + 113/24) + 61/17 sin(7 t + 65/41) + 151/33 sin(8 t + 30/19) + 70/31 sin(9 t + 179/38) + 101/19 sin(10 t + 35/22) + 31/35 sin(11 t + 35/22) + 47/55 sin(13 t + 49/31) + 13/53 sin(14 t + 37/24) + 30/47 sin(15 t + 38/23) + 65/38 sin(16 t + 35/22) + 1/39 sin(18 t + 95/27) + 118/119 sin(19 t + 49/30) + 27/107 sin(20 t + 13/8) + 15/44 sin(24 t + 61/13) + 11/10 sin(25 t + 61/37) + 27/29 sin(26 t + 23/14) + 2/17 sin(28 t + 29/26) + 2/33 sin(29 t + 45/31) + 15/23 sin(30 t + 72/43) + 25/24 sin(31 t + 51/31) - 777/26) θ(83 π - t) θ(t - 79 π) + (-1/63 sin(59/38 - 10 t) + 66/37 sin(t + 11/7) + 13/5 sin(2 t + 11/7) + 8/15 sin(3 t + 245/52) + 7/34 sin(4 t + 41/26) + 4/21 sin(5 t + 41/26) + 1/13 sin(6 t + 30/19) + 3/26 sin(7 t + 146/31) + 3/22 sin(8 t + 30/19) + 1/240 sin(9 t + 114/25) + 1/749 sin(11 t + 38/23) + 1/19 sin(12 t + 49/31) + 5462/47) θ(79 π - t) θ(t - 75 π) + (-3/11 sin(208/139 - 12 t) - 9/34 sin(67/43 - 10 t) - 49/45 sin(43/28 - 9 t) - 287/76 sin(14/9 - 6 t) - 49/17 sin(37/24 - 5 t) - 373/33 sin(25/16 - 4 t) - 282/29 sin(61/39 - 3 t) + 23/10 sin(t + 221/47) + 1540/81 sin(2 t + 11/7) + 3/7 sin(7 t + 53/34) + 28/111 sin(8 t + 91/61) + 7/36 sin(11 t + 44/29) + 1694/13) θ(75 π - t) θ(t - 71 π) + (-3/17 sin(39/25 - 11 t) - 19/33 sin(39/25 - 8 t) - 40/21 sin(80/51 - 3 t) - 32/29 sin(36/23 - 2 t) + 25/9 sin(t + 11/7) + 105/23 sin(4 t + 63/40) + 85/64 sin(5 t + 52/33) + 5/18 sin(6 t + 30/19) + 5/18 sin(7 t + 68/43) + 5/32 sin(9 t + 36/23) + 4/35 sin(10 t + 146/31) + 3/20 sin(12 t + 11/7) + 816/11) θ(71 π - t) θ(t - 67 π) + (-83/35 sin(48/31 - 9 t) - 709/32 sin(39/25 - 2 t) - 7/36 sin(41/35 - t) + 392/37 sin(3 t + 35/22) + 382/25 sin(4 t + 51/32) + 32/13 sin(5 t + 75/16) + 174/25 sin(6 t + 8/5) + 13/6 sin(7 t + 163/98) + 46/19 sin(8 t + 35/22) + 25/14 sin(10 t + 49/31) + 5/46 sin(11 t + 73/20) + 1029/514 sin(12 t + 73/45) + 6142/91) θ(67 π - t) θ(t - 63 π) + (-62/61 sin(36/23 - 10 t) - 34/37 sin(45/29 - 8 t) - 233/155 sin(47/30 - 6 t) - 59/21 sin(36/23 - 5 t) - 335/38 sin(47/30 - 4 t) - 101/8 sin(69/44 - 2 t) + 123/5 sin(t + 212/45) + 543/40 sin(3 t + 91/58) + 7/50 sin(7 t + 70/51) + 33/37 sin(9 t + 11/7) + 11/15 sin(11 t + 30/19) + 30/121 sin(12 t + 19/12) + 1378/21) θ(63 π - t) θ(t - 59 π) + (-8/23 sin(36/23 - 11 t) - 11/27 sin(36/23 - 10 t) - 43/85 sin(47/30 - 8 t) - 45/31 sin(11/7 - 6 t) + 355/46 sin(t + 146/31) + 499/35 sin(2 t + 245/52) + 61/31 sin(3 t + 11/7) + 45/134 sin(4 t + 47/10) + 32/39 sin(5 t + 212/45) + 11/9 sin(7 t + 69/44) + 13/32 sin(9 t + 113/24) + 9/22 sin(12 t + 47/10) + 1517/24) θ(59 π - t) θ(t - 55 π) + (-89/38 sin(45/29 - 9 t) - 119/39 sin(36/23 - 5 t) - 52/41 sin(53/34 - 2 t) - 292/35 sin(36/23 - t) + 164/17 sin(3 t + 19/12) + 377/34 sin(4 t + 30/19) + 102/37 sin(6 t + 52/33) + 53/66 sin(7 t + 67/41) + 33/35 sin(8 t + 11/7) + 2/13 sin(10 t + 48/31) + 47/37 sin(11 t + 50/31) + 11/19 sin(12 t + 21/13) + 33/67) θ(55 π - t) θ(t - 51 π) + (1494/17 sin(t + 52/33) + 70 sin(2 t + 49/31) + 1004/25 sin(3 t + 27/17) + 100/13 sin(4 t + 191/41) + 38/39 sin(5 t + 207/49) + 162/17 sin(6 t + 57/35) + 59/23 sin(7 t + 47/27) + 193/26 sin(8 t + 13/8) + 283/63 sin(9 t + 75/16) + 65/32 sin(10 t + 57/35) + 116/83 sin(11 t + 51/31) + 91/45 sin(12 t + 66/41) + 13/51 sin(13 t + 291/145) + 195/71 sin(14 t + 18/11) + 103/72 sin(15 t + 97/21) + 65/24 sin(16 t + 57/34) + 16/29 sin(17 t + 68/33) + 24/49 sin(18 t + 49/24) + 3/11 sin(19 t + 131/34) + 17/16 sin(20 t + 37/21) + 13/14 sin(21 t + 26/15) + 57/43 sin(22 t + 93/56) + 16/43 sin(23 t + 107/23) + 25/42 sin(24 t + 83/51) - 925/13) θ(51 π - t) θ(t - 47 π) + (-34/29 sin(37/24 - 12 t) - 7/17 sin(43/28 - 9 t) - 62/23 sin(45/29 - 6 t) - 151/42 sin(36/23 - 4 t) - 13/42 sin(19/20 - 3 t) - 903/26 sin(53/34 - 2 t) - 212/29 sin(57/37 - t) + 39/23 sin(5 t + 11/7) + 37/39 sin(7 t + 53/34) + 12/31 sin(8 t + 80/17) + 8/25 sin(10 t + 43/25) + 48/41 sin(11 t + 45/28) + 18/25 sin(13 t + 27/17) + 7/20 sin(14 t + 53/30) + 1/8 sin(15 t + 29/17) + 4/19 sin(16 t + 19/11) + 26/51 sin(17 t + 59/36) + 1/11 sin(18 t + 67/15) + 7/20 sin(19 t + 28/17) + 9905/41) θ(47 π - t) θ(t - 43 π) + (-8/9 sin(45/31 - 18 t) - 181/25 sin(36/23 - 12 t) - 775/21 sin(113/72 - 6 t) + 2756/63 sin(t + 113/24) + 165/29 sin(2 t + 30/19) + 2083/35 sin(3 t + 212/45) + 617/16 sin(4 t + 47/30) + 610/17 sin(5 t + 47/30) + 995/32 sin(7 t + 58/37) + 155/24 sin(8 t + 54/35) + 359/25 sin(9 t + 36/23) + 49/22 sin(10 t + 26/17) + 34/15 sin(11 t + 192/41) + 441/43 sin(13 t + 69/44) + 101/16 sin(14 t + 127/27) + 341/35 sin(15 t + 202/43) + 115/28 sin(16 t + 89/19) + 11/6 sin(17 t + 35/22) + 82/33 sin(19 t + 39/25) + 134/63 sin(20 t + 75/16) + 40/37 sin(21 t + 32/7) + 18/53 sin(22 t + 91/20) + 6/7 sin(23 t + 59/38) + 37/36 sin(24 t + 41/28) + 89/33 sin(25 t + 45/29) + 57/28 sin(26 t + 155/33) + 15/38 sin(27 t + 83/18) + 29/47 sin(28 t + 121/26) + 23/20 sin(29 t + 257/55) + 37/25 sin(30 t + 136/29) + 21/32 sin(31 t + 21/13) + 37/35 sin(32 t + 47/10) + 3/19 sin(33 t + 83/51) + 19/77 sin(34 t + 49/30) + 5/28 sin(35 t + 38/25) + 7/15 sin(36 t + 189/41) + 6/11 sin(37 t + 55/37) + 15/23 sin(38 t + 179/38) + 19/24 sin(39 t + 59/38) + 19210/103) θ(43 π - t) θ(t - 39 π) + (-19/27 sin(58/37 - 25 t) - 195/62 sin(136/91 - 23 t) - 31/26 sin(47/34 - 22 t) - 23/17 sin(31/21 - 21 t) - 48/17 sin(236/157 - 19 t) - 100/31 sin(23/15 - 17 t) - 35/13 sin(28/19 - 16 t) - 97/36 sin(14/9 - 9 t) - 366/31 sin(20/13 - 8 t) - 348/31 sin(45/29 - 7 t) - 1241/43 sin(47/30 - 2 t) - 18/31 sin(38/27 - t) + 2218/69 sin(3 t + 30/19) + 113/25 sin(4 t + 47/10) + 137/10 sin(5 t + 27/17) + 149/35 sin(6 t + 43/27) + 503/39 sin(10 t + 21/13) + 269/17 sin(11 t + 50/31) + 121/40 sin(12 t + 179/38) + 7/31 sin(13 t + 28/15) + 35/6 sin(14 t + 49/30) + 4/31 sin(15 t + 95/22) + 76/35 sin(18 t + 27/17) + 25/28 sin(20 t + 61/41) + 27/26 sin(24 t + 43/27) - 294/13) θ(39 π - t) θ(t - 35 π) + (-29/48 sin(112/75 - 23 t) - 21/25 sin(14/9 - 21 t) - 49/29 sin(54/35 - 20 t) - 67/23 sin(55/36 - 16 t) - 633/79 sin(67/43 - 14 t) - 137/23 sin(20/13 - 13 t) - 48/23 sin(32/21 - 11 t) - 225/23 sin(45/29 - 10 t) - 397/40 sin(31/20 - 8 t) - 341/57 sin(39/25 - 7 t) - 779/37 sin(61/39 - 6 t) - 2/33 sin(5/12 - 5 t) - 281/16 sin(25/16 - 4 t) - 1549/25 sin(47/30 - 2 t) - 7338/179 sin(80/51 - t) + 361/72 sin(3 t + 63/40) + 907/53 sin(9 t + 65/41) + 383/31 sin(12 t + 43/27) + 9/4 sin(15 t + 221/47) + 141/37 sin(17 t + 43/27) + 7/32 sin(18 t + 75/43) + 82/25 sin(19 t + 35/22) + 6/25 sin(22 t + 78/17) + 9/17 sin(24 t + 12/7) + 8/27 sin(25 t + 61/42) + 2891/22) θ(35 π - t) θ(t - 31 π) + (-12/19 sin(71/46 - 14 t) - 4/27 sin(44/29 - 12 t) - 395/38 sin(31/20 - 8 t) + 35/6 sin(t + 19/12) + 4663/68 sin(2 t + 52/33) + 6/53 sin(3 t + 8/3) + 513/17 sin(4 t + 30/19) + 101/36 sin(5 t + 60/37) + 89/8 sin(6 t + 19/12) + 22/13 sin(7 t + 47/10) + 1125/562 sin(9 t + 13/8) + 283/24 sin(10 t + 43/27) + 55/83 sin(11 t + 157/34) + 1/11 sin(13 t + 29/16) + 1/4 sin(15 t + 37/8) + 103/44 sin(16 t + 53/33) + 21/85 sin(17 t + 72/41) + 11/17 sin(18 t + 29/18) + 5/28 sin(19 t + 119/26) + 11/37 sin(20 t + 51/31) - 5657/24) θ(31 π - t) θ(t - 27 π) + (-724/167 sin(53/34 - 12 t) - 133/59 sin(36/23 - 11 t) - 355/118 sin(43/28 - 5 t) + 578/37 sin(t + 30/19) + 2546/23 sin(2 t + 179/38) + 290/21 sin(3 t + 41/26) + 203/30 sin(4 t + 59/38) + 369/17 sin(6 t + 102/65) + 322/31 sin(7 t + 146/31) + 524/31 sin(8 t + 80/17) + 177/31 sin(9 t + 193/41) + 19/14 sin(10 t + 43/27) + 43/42 sin(13 t + 8/5) + 29/13 sin(14 t + 212/45) + 69/43 sin(15 t + 155/33) + 32/15 sin(16 t + 127/27) + 158/33 sin(17 t + 113/24) + 87/34 sin(18 t + 89/19) + 101/72 sin(19 t + 61/13) + 49/23 sin(20 t + 127/27) - 5391/50) θ(27 π - t) θ(t - 23 π) + (-13/59 sin(25/16 - 16 t) - 9/22 sin(31/20 - 11 t) - 17/27 sin(39/25 - 10 t) - 24/17 sin(25/16 - 8 t) - 3/14 sin(54/35 - 7 t) - 45/46 sin(45/29 - 5 t) - 189/47 sin(58/37 - 4 t) - 503/27 sin(113/72 - 2 t) - 682/27 sin(102/65 - t) + 207/28 sin(3 t + 107/68) + 7/30 sin(6 t + 64/41) + 27/32 sin(9 t + 52/33) + 4/29 sin(12 t + 21/13) + 1/4 sin(13 t + 68/43) + 8/35 sin(14 t + 179/38) + 7/20 sin(15 t + 30/19) + 5/38 sin(17 t + 113/24) + 1/94 sin(18 t + 104/23) + 1/16 sin(19 t + 37/23) - 18999/43) θ(23 π - t) θ(t - 19 π) + (-41/37 sin(58/37 - 17 t) - 23/7 sin(31/20 - 15 t) - 86/85 sin(325/217 - 14 t) - 38/13 sin(59/38 - 13 t) - 86/53 sin(58/37 - 11 t) - 289/14 sin(39/25 - 5 t) - 895/13 sin(58/37 - t) + 634/45 sin(2 t + 63/40) + 994/27 sin(3 t + 30/19) + 227/12 sin(4 t + 30/19) + 203/23 sin(6 t + 19/12) + 202/47 sin(7 t + 101/63) + 336/55 sin(8 t + 30/19) + 99/10 sin(9 t + 43/27) + 322/31 sin(10 t + 27/17) + 67/23 sin(12 t + 49/31) + 23/39 sin(16 t + 48/31) + 34/39 sin(18 t + 51/32) + 43/17 sin(19 t + 47/29) + 43/40 sin(20 t + 30/19) - 18457/41) θ(19 π - t) θ(t - 15 π) + (-2/11 sin(51/35 - 16 t) - 5/13 sin(71/52 - 14 t) - 181/30 sin(47/30 - 10 t) - 800/13 sin(102/65 - t) + 1942/27 sin(2 t + 69/44) + 245/12 sin(3 t + 80/51) + 816/25 sin(4 t + 179/38) + 52/27 sin(5 t + 41/25) + 313/22 sin(6 t + 113/24) + 353/39 sin(7 t + 52/33) + 143/14 sin(8 t + 179/38) + 155/24 sin(9 t + 41/26) + 99/20 sin(11 t + 36/23) + 77/32 sin(12 t + 68/45) + 75/13 sin(13 t + 39/25) + 13/11 sin(15 t + 164/35) + 5/14 sin(17 t + 47/31) + 28/47 sin(18 t + 53/35) + 74/73 sin(19 t + 37/24) + 5/22 sin(20 t + 93/20) - 22534/83) θ(15 π - t) θ(t - 11 π) + (-11/23 sin(29/20 - 23 t) - 83/24 sin(69/44 - 21 t) - 151/28 sin(87/56 - 19 t) - 274/25 sin(14/9 - 17 t) - 41/21 sin(63/44 - 14 t) - 51/46 sin(37/29 - 12 t) - 2065/99 sin(39/25 - 11 t) + 5424/41 sin(t + 80/51) + 7812/41 sin(2 t + 91/58) + 2605/84 sin(3 t + 19/12) + 1053/4 sin(4 t + 102/65) + 2386/23 sin(5 t + 212/45) + 1792/33 sin(6 t + 155/33) + 409/31 sin(7 t + 32/21) + 729/56 sin(8 t + 133/83) + 57/14 sin(9 t + 45/29) + 109/17 sin(10 t + 41/26) + 478/25 sin(13 t + 169/36) + 56/25 sin(15 t + 194/129) + 5/4 sin(16 t + 75/16) + 135/47 sin(18 t + 127/27) + 19/35 sin(20 t + 8/5) + 61/32 sin(22 t + 49/30) + 17/31 sin(24 t + 95/21) + 36/23 sin(25 t + 61/13) + 39/17 sin(26 t + 46/29) + 64/51 sin(27 t + 63/38) + 40/43 sin(28 t + 59/40) + 5/19 sin(29 t + 157/35) + 20/7 sin(30 t + 23/15) + 482/481 sin(31 t + 208/45) + 90/91 sin(32 t + 61/39) + 18/19 sin(33 t + 31/22) + 18/29 sin(34 t + 39/22) + 32/63 sin(35 t + 37/25) + 1/30 sin(36 t + 176/43) + 20/13 sin(37 t + 499/107) + 10/27 sin(38 t + 59/41) + 3/2 sin(39 t + 75/16) + 1/86 sin(40 t + 23/28) - 29249/41) θ(11 π - t) θ(t - 7 π) + (-46/29 sin(26/17 - 12 t) - 15/19 sin(31/20 - 11 t) - 67/6 sin(36/23 - 7 t) - 466/17 sin(58/37 - 3 t) + 1217/33 sin(t + 118/75) + 1306/95 sin(2 t + 11/7) + 867/43 sin(4 t + 85/54) + 176/13 sin(5 t + 30/19) + 959/101 sin(6 t + 41/26) + 207/28 sin(8 t + 11/7) + 66/31 sin(9 t + 93/58) + 291/37 sin(10 t + 19/12) - 104662/97) θ(7 π - t) θ(t - 3 π) + (-108/43 sin(59/38 - 12 t) - 11/9 sin(73/47 - 11 t) - 457/19 sin(61/39 - 4 t) + 283/14 sin(t + 212/45) + 458/7 sin(2 t + 74/47) + 307/35 sin(3 t + 85/54) + 541/116 sin(5 t + 36/23) + 273/32 sin(6 t + 30/19) + 191/22 sin(7 t + 19/12) + 183/14 sin(8 t + 68/43) + 121/31 sin(9 t + 62/39) + 58/19 sin(10 t + 74/47) - 34942/29) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2))))
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