Computing...

Input interpretation:

Downward Facing Dog Pose yoga curve  (popular curve)


Alternate names:

Adho Mukha Svanasana curve  |  Down Dog Pose yoga curve  |  Downward Dog Pose yoga curve


Associated yoga pose:

Downward Facing Dog Pose


Equations:

Parametric equations:

x(t) = ((-2\/5 sin(11\/7 - 5 t) + 94\/11 sin(t + 11\/7) + 12\/7 sin(2 t + 11\/7) + 4\/13 sin(3 t + 33\/7) + 9\/8 sin(4 t + 11\/7) + 11\/21 sin(6 t + 11\/7) + 875\/8) theta(67 pi - t) theta(t - 63 pi) + (-1\/28 sin(3\/2 - 27 t) - 1\/24 sin(3\/2 - 26 t) - 1\/25 sin(17\/11 - 18 t) - 2\/5 sin(17\/11 - 13 t) - 14\/27 sin(14\/9 - 12 t) - 1\/4 sin(14\/9 - 11 t) - 1\/11 sin(20\/13 - 10 t) - 1\/11 sin(26\/17 - 9 t) - 1\/11 sin(11\/7 - 8 t) - sin(11\/7 - 4 t) - 106\/15 sin(11\/7 - t) + 28\/29 sin(2 t + 11\/7) + 7\/9 sin(3 t + 11\/7) + 1\/84 sin(5 t + 47\/10) + 3\/10 sin(6 t + 11\/7) + 1\/9 sin(7 t + 47\/10) + 1\/16 sin(14 t + 11\/7) + 1\/3 sin(15 t + 8\/5) + 1\/4 sin(16 t + 8\/5) + 1\/37 sin(17 t + 14\/9) + 1\/14 sin(19 t + 13\/8) + 1\/7 sin(20 t + 21\/13) + 1\/11 sin(21 t + 8\/5) + 1\/63 sin(22 t + 32\/21) + 1\/41 sin(23 t + 8\/5) + 1\/21 sin(24 t + 13\/8) + 1\/46 sin(28 t + 19\/12) + 1\/16 sin(29 t + 8\/5) + 1\/32 sin(30 t + 8\/5) + 1\/55 sin(33 t + 13\/8) + 1418\/13) theta(63 pi - t) theta(t - 59 pi) + (-1\/49 sin(4\/3 - 30 t) - 1\/13 sin(35\/23 - 27 t) - 1\/9 sin(35\/23 - 25 t) - 1\/7 sin(20\/13 - 23 t) - 2\/9 sin(32\/21 - 21 t) - 2\/11 sin(29\/19 - 19 t) - 2\/9 sin(23\/15 - 17 t) - 1\/7 sin(14\/9 - 15 t) - 1\/79 sin(13\/11 - 14 t) - 2\/9 sin(17\/11 - 13 t) - 1\/21 sin(3\/2 - 12 t) - 2\/7 sin(3\/2 - 10 t) - 5\/9 sin(17\/11 - 9 t) - 3\/4 sin(17\/11 - 6 t) - 3\/2 sin(14\/9 - 5 t) - 99\/8 sin(11\/7 - 2 t) + 37\/6 sin(t + 11\/7) + 5\/6 sin(3 t + 11\/7) + 5\/7 sin(4 t + 19\/12) + 1\/26 sin(7 t + 14\/3) + 2\/9 sin(8 t + 8\/5) + 1\/27 sin(11 t + 13\/8) + 1\/24 sin(16 t + 32\/21) + 1\/6 sin(18 t + 13\/8) + 1\/12 sin(20 t + 14\/9) + 1\/8 sin(22 t + 8\/5) + 1\/17 sin(24 t + 17\/11) + 1\/27 sin(26 t + 3\/2) + 1\/58 sin(29 t + 65\/14) + 2267\/18) theta(59 pi - t) theta(t - 55 pi) + (-1\/57 sin(29\/19 - 28 t) - 3\/10 sin(11\/7 - 6 t) - 2\/9 sin(14\/9 - 4 t) - 55\/54 sin(11\/7 - 3 t) - 57\/7 sin(11\/7 - 2 t) + 8\/7 sin(t + 33\/7) + 6\/11 sin(5 t + 11\/7) + 1\/38 sin(7 t + 14\/9) + 1\/20 sin(8 t + 14\/3) + 4\/9 sin(9 t + 19\/12) + 1\/10 sin(10 t + 13\/8) + 3\/14 sin(11 t + 11\/7) + 1\/21 sin(12 t + 18\/11) + 2\/11 sin(13 t + 19\/12) + 1\/10 sin(14 t + 21\/13) + 2\/11 sin(15 t + 8\/5) + 1\/18 sin(16 t + 21\/13) + 1\/8 sin(17 t + 8\/5) + 1\/19 sin(18 t + 18\/11) + 1\/9 sin(19 t + 19\/12) + 1\/20 sin(20 t + 23\/14) + 1\/17 sin(21 t + 19\/12) + 1\/26 sin(23 t + 8\/5) + 1\/18 sin(25 t + 8\/5) + 1\/94 sin(26 t + 17\/10) + 1\/35 sin(27 t + 19\/12) + 1259\/11) theta(55 pi - t) theta(t - 51 pi) + (-1\/28 sin(17\/11 - 28 t) - 1\/20 sin(17\/11 - 24 t) - 1\/15 sin(17\/11 - 22 t) - 1\/42 sin(15\/11 - 21 t) - 1\/11 sin(14\/9 - 19 t) - 1\/29 sin(18\/13 - 17 t) - 1\/38 sin(11\/8 - 16 t) - 1\/88 sin(20\/19 - 15 t) - 1\/6 sin(14\/9 - 14 t) - 4\/15 sin(11\/7 - 12 t) - 3\/5 sin(14\/9 - 10 t) - 9\/8 sin(14\/9 - 8 t) - 7\/6 sin(11\/7 - 6 t) - 1\/10 sin(19\/13 - 5 t) - 34\/11 sin(14\/9 - 4 t) - 53\/15 sin(14\/9 - 3 t) - 19\/4 sin(14\/9 - 2 t) - 104\/3 sin(11\/7 - t) + 4\/3 sin(7 t + 11\/7) + 1\/3 sin(9 t + 17\/11) + 4\/11 sin(11 t + 11\/7) + 1\/9 sin(13 t + 19\/12) + 1\/10 sin(18 t + 5\/3) + 1\/21 sin(20 t + 19\/12) + 1\/16 sin(23 t + 8\/5) + 1\/11 sin(25 t + 8\/5) + 1\/15 sin(26 t + 33\/7) + 1\/15 sin(27 t + 8\/5) + 1\/21 sin(29 t + 13\/8) + 901\/11) theta(51 pi - t) theta(t - 47 pi) + (-1\/9 sin(14\/9 - 24 t) - 1\/65 sin(5\/4 - 16 t) - 1\/19 sin(17\/11 - 6 t) + 179\/6 sin(t + 11\/7) + 58\/9 sin(2 t + 11\/7) + 33\/8 sin(3 t + 11\/7) + 11\/10 sin(4 t + 33\/7) + 17\/11 sin(5 t + 11\/7) + 8\/11 sin(7 t + 11\/7) + 5\/8 sin(8 t + 14\/9) + 3\/8 sin(9 t + 47\/10) + 6\/13 sin(10 t + 17\/11) + 8\/11 sin(11 t + 14\/9) + 7\/13 sin(12 t + 47\/10) + 7\/15 sin(13 t + 14\/9) + 1\/15 sin(14 t + 10\/7) + 2\/9 sin(15 t + 11\/7) + 1\/19 sin(17 t + 17\/10) + 1\/9 sin(18 t + 34\/23) + 2\/7 sin(19 t + 14\/9) + 3\/13 sin(20 t + 61\/13) + 1\/5 sin(21 t + 14\/9) + 1\/7 sin(23 t + 14\/9) + 1\/19 sin(25 t + 8\/5) + 1\/9 sin(26 t + 38\/25) + 1\/76 sin(27 t + 22\/5) + 1\/64 sin(28 t + 51\/11) + 1\/8 sin(29 t + 32\/21) + 371\/6) theta(47 pi - t) theta(t - 43 pi) + (-1\/23 sin(20\/13 - 22 t) - 1\/8 sin(26\/17 - 20 t) - 1\/14 sin(28\/19 - 18 t) - 2\/9 sin(17\/11 - 14 t) - 1\/8 sin(23\/15 - 13 t) - 1\/5 sin(38\/25 - 12 t) - 7\/13 sin(14\/9 - 10 t) - 18\/11 sin(11\/7 - 6 t) - 7\/9 sin(26\/17 - 5 t) - 44\/19 sin(17\/11 - 4 t) - 619\/31 sin(11\/7 - 2 t) - 55\/6 sin(11\/7 - t) + 172\/57 sin(3 t + 14\/9) + 16\/13 sin(7 t + 11\/7) + 2\/3 sin(8 t + 33\/7) + 3\/13 sin(9 t + 14\/3) + 3\/4 sin(11 t + 11\/7) + 3\/13 sin(15 t + 8\/5) + 1\/9 sin(16 t + 33\/7) + 1\/18 sin(17 t + 47\/10) + 1\/12 sin(19 t + 3\/2) + 1\/16 sin(23 t + 18\/11) + 1\/8 sin(24 t + 33\/7) + 23) theta(43 pi - t) theta(t - 39 pi) + (-3\/11 sin(11\/7 - 3 t) - 3\/4 sin(11\/7 - 2 t) + 7\/12 sin(t + 11\/7) + 1\/12 sin(4 t + 11\/7) + 1\/9 sin(5 t + 19\/12) + 1\/9 sin(6 t + 11\/7) + 1\/11 sin(7 t + 19\/12) + 1\/61 sin(8 t + 21\/13) + 1\/21 sin(9 t + 19\/12) + 1\/18 sin(10 t + 8\/5) - 189\/11) theta(39 pi - t) theta(t - 35 pi) + (-1\/60 sin(11\/7 - 5 t) - 1\/20 sin(14\/9 - 4 t) - 3\/14 sin(11\/7 - 3 t) + 1\/9 sin(t + 11\/7) + 2\/13 sin(2 t + 11\/7) + 1\/24 sin(6 t + 11\/7) + 1\/99 sin(7 t + 19\/12) - 631\/30) theta(35 pi - t) theta(t - 31 pi) + (-1\/3 sin(11\/7 - 6 t) - 4\/13 sin(11\/7 - 4 t) - 23\/9 sin(11\/7 - 2 t) - 2\/5 sin(11\/7 - t) + 1\/16 sin(3 t + 33\/7) + 1\/9 sin(5 t + 11\/7) - 56\/9) theta(31 pi - t) theta(t - 27 pi) + (-1\/15 sin(11\/7 - 24 t) - 1\/11 sin(14\/9 - 18 t) - 1\/2 sin(11\/7 - 8 t) - 7\/2 sin(11\/7 - 2 t) + 71\/7 sin(t + 11\/7) + 12\/11 sin(3 t + 11\/7) + 1\/8 sin(4 t + 32\/21) + 8\/5 sin(5 t + 11\/7) + 5\/9 sin(6 t + 11\/7) + 2\/9 sin(7 t + 11\/7) + 1\/7 sin(9 t + 11\/7) + 1\/13 sin(10 t + 47\/10) + 1\/14 sin(11 t + 8\/5) + 1\/6 sin(12 t + 11\/7) + 1\/14 sin(13 t + 11\/7) + 1\/8 sin(14 t + 33\/7) + 1\/6 sin(15 t + 11\/7) + 1\/11 sin(16 t + 11\/7) + 1\/60 sin(17 t + 18\/11) + 1\/18 sin(19 t + 11\/7) + 1\/60 sin(20 t + 14\/3) + 1\/30 sin(21 t + 14\/9) + 1\/12 sin(22 t + 8\/5) + 1\/52 sin(23 t + 3\/2) + 1\/16 sin(25 t + 11\/7) - 81\/8) theta(27 pi - t) theta(t - 23 pi) + (-8\/17 sin(11\/7 - 3 t) + 22\/9 sin(t + 11\/7) + 13\/5 sin(2 t + 11\/7) + 2\/7 sin(4 t + 11\/7) + 2\/9 sin(5 t + 19\/12) + 1\/7 sin(6 t + 11\/7) + 1\/8 sin(7 t + 33\/7) + 2\/11 sin(8 t + 11\/7) - 607\/9) theta(23 pi - t) theta(t - 19 pi) + (-1\/40 sin(28\/19 - 27 t) - 1\/10 sin(35\/23 - 24 t) - 3\/8 sin(14\/9 - 18 t) - 6\/17 sin(11\/7 - 17 t) - 3\/10 sin(17\/11 - 14 t) - 2\/3 sin(14\/9 - 11 t) - 51\/19 sin(11\/7 - 3 t) - 61\/5 sin(11\/7 - t) + 20\/3 sin(2 t + 11\/7) + 33\/14 sin(4 t + 11\/7) + 1\/6 sin(5 t + 33\/7) + 5\/9 sin(6 t + 33\/7) + 5\/7 sin(7 t + 14\/9) + 18\/7 sin(8 t + 11\/7) + 18\/11 sin(9 t + 11\/7) + 8\/17 sin(10 t + 11\/7) + 3\/8 sin(12 t + 19\/12) + 7\/15 sin(13 t + 8\/5) + 4\/11 sin(15 t + 47\/10) + 1\/3 sin(16 t + 8\/5) + 1\/3 sin(19 t + 11\/7) + 3\/7 sin(20 t + 19\/12) + 1\/57 sin(21 t + 10\/9) + 1\/8 sin(22 t + 21\/13) + 1\/33 sin(23 t + 32\/7) + 1\/13 sin(25 t + 13\/8) + 1\/6 sin(26 t + 14\/9) + 2\/11 sin(28 t + 11\/7) + 1\/8 sin(29 t + 19\/12) - 269\/4) theta(19 pi - t) theta(t - 15 pi) + (-1\/12 sin(3\/2 - 30 t) - 1\/9 sin(22\/15 - 26 t) - 2\/11 sin(3\/2 - 23 t) - 1\/9 sin(14\/9 - 18 t) - 2\/7 sin(11\/7 - 14 t) - 11\/5 sin(14\/9 - 8 t) + 145\/17 sin(t + 11\/7) + 34\/9 sin(2 t + 11\/7) + 20\/9 sin(3 t + 11\/7) + 19\/8 sin(4 t + 11\/7) + 17\/14 sin(5 t + 14\/9) + 17\/11 sin(6 t + 19\/12) + 3\/7 sin(7 t + 47\/10) + 13\/7 sin(9 t + 19\/12) + 1\/9 sin(10 t + 13\/9) + 3\/7 sin(11 t + 14\/9) + 1\/7 sin(12 t + 61\/13) + 1\/33 sin(13 t + 9\/5) + 1\/38 sin(15 t + 17\/12) + 2\/7 sin(16 t + 8\/5) + 1\/10 sin(17 t + 3\/2) + 1\/39 sin(21 t + 47\/10) + 1\/12 sin(22 t + 19\/11) + 1\/17 sin(24 t + 19\/12) + 1\/6 sin(25 t + 21\/13) + 1\/49 sin(27 t + 25\/14) + 1\/10 sin(28 t + 61\/13) - 3994\/47) theta(15 pi - t) theta(t - 11 pi) + (-1\/12 sin(4\/3 - 20 t) - 1\/6 sin(3\/2 - 15 t) - 1\/5 sin(10\/7 - 14 t) - 4\/9 sin(28\/19 - 13 t) - 1\/6 sin(19\/14 - 12 t) - 1\/15 sin(25\/17 - 11 t) - 86\/85 sin(17\/11 - 7 t) - 3\/4 sin(35\/23 - 6 t) - 13\/8 sin(17\/11 - 5 t) - 2\/9 sin(23\/17 - 4 t) - 62\/25 sin(17\/11 - 3 t) - 22 sin(11\/7 - t) + 20\/19 sin(2 t + 32\/21) + 1\/10 sin(8 t + 19\/12) + 1\/7 sin(9 t + 17\/10) + 3\/7 sin(10 t + 8\/5) + 1\/10 sin(16 t + 13\/8) + 1\/13 sin(17 t + 16\/9) + 1\/6 sin(18 t + 28\/17) + 1\/33 sin(19 t + 61\/13) - 865\/13) theta(11 pi - t) theta(t - 7 pi) + (-1\/32 sin(29\/19 - 34 t) - 1\/26 sin(14\/9 - 33 t) - 1\/27 sin(14\/9 - 31 t) - 1\/18 sin(3\/2 - 26 t) - 1\/9 sin(14\/9 - 25 t) - 1\/9 sin(3\/2 - 23 t) - 3\/7 sin(14\/9 - 19 t) - 1\/3 sin(29\/19 - 15 t) - 6\/17 sin(11\/7 - 13 t) - 3\/4 sin(20\/13 - 9 t) - 35\/13 sin(14\/9 - 5 t) + 16\/9 sin(t + 14\/3) + 127\/5 sin(2 t + 33\/7) + 163\/18 sin(3 t + 33\/7) + 43\/11 sin(4 t + 11\/7) + 9\/11 sin(6 t + 79\/17) + 30\/7 sin(7 t + 47\/10) + 3\/4 sin(8 t + 21\/13) + 5\/14 sin(10 t + 8\/5) + 3\/7 sin(11 t + 14\/3) + 2\/9 sin(12 t + 33\/7) + 2\/9 sin(14 t + 51\/11) + 1\/4 sin(16 t + 14\/9) + 4\/7 sin(17 t + 61\/13) + 1\/6 sin(18 t + 7\/4) + 3\/11 sin(20 t + 21\/13) + 10\/21 sin(21 t + 47\/10) + 1\/27 sin(22 t + 17\/9) + 1\/10 sin(24 t + 8\/5) + 1\/18 sin(27 t + 32\/7) + 1\/11 sin(28 t + 14\/3) + 1\/22 sin(29 t + 32\/7) + 1\/16 sin(32 t + 37\/8) + 1\/84 sin(35 t + 5\/2) + 1\/14 sin(36 t + 14\/3) + 1\/27 sin(37 t + 14\/3) - 683\/31) theta(7 pi - t) theta(t - 3 pi) + (-1\/56 sin(4\/5 - 19 t) - 1\/29 sin(7\/12 - 18 t) - 1\/21 sin(9\/10 - 9 t) - 1\/6 sin(2\/3 - 8 t) - 1\/9 sin(7\/5 - 7 t) - 3\/5 sin(49\/50 - 5 t) + 44\/9 sin(t + 11\/10) + 8\/7 sin(2 t + 24\/11) + 14\/15 sin(3 t + 11\/10) + 2\/5 sin(4 t + 1\/8) + 11\/17 sin(6 t + 15\/11) + 1\/7 sin(10 t + 27\/13) + 1\/8 sin(11 t + 37\/8) + 1\/12 sin(12 t + 11\/8) + 1\/20 sin(13 t + 93\/46) + 1\/25 sin(14 t + 1\/11) + 1\/25 sin(15 t + 14\/3) + 1\/12 sin(16 t + 7\/5) + 1\/58 sin(17 t + 15\/8) - 321\/8) theta(3 pi - t) theta(t + pi)) theta(sqrt(sgn(sin(t\/2))))\ny(t) = ((-1\/53 sin(11\/7 - 6 t) - 1\/5 sin(11\/7 - 3 t) - 1\/2 sin(11\/7 - t) + 7\/8 sin(2 t + 11\/7) + 1\/3 sin(4 t + 11\/7) + 1\/17 sin(5 t + 19\/12) - 393\/13) theta(67 pi - t) theta(t - 63 pi) + (-1\/22 sin(20\/13 - 27 t) - 1\/44 sin(20\/13 - 26 t) - 1\/33 sin(14\/9 - 25 t) - 1\/25 sin(14\/9 - 23 t) - 1\/25 sin(17\/11 - 19 t) - 1\/31 sin(14\/9 - 17 t) - 2\/11 sin(14\/9 - 15 t) - 1\/9 sin(23\/15 - 14 t) - 1\/6 sin(14\/9 - 9 t) - 1\/8 sin(11\/7 - 7 t) - 121\/61 sin(11\/7 - 3 t) - 77\/12 sin(11\/7 - t) + 28\/11 sin(2 t + 11\/7) + 7\/11 sin(4 t + 11\/7) + 4\/11 sin(5 t + 33\/7) + 1\/9 sin(6 t + 14\/9) + 1\/12 sin(8 t + 8\/5) + 1\/8 sin(10 t + 11\/7) + 1\/9 sin(11 t + 33\/7) + 1\/9 sin(13 t + 33\/7) + 1\/89 sin(18 t + 8\/5) + 1\/42 sin(21 t + 47\/10) + 1\/67 sin(22 t + 14\/9) + 1\/45 sin(30 t + 13\/8) - 47\/2) theta(63 pi - t) theta(t - 59 pi) + (-1\/21 sin(26\/17 - 30 t) - 1\/24 sin(14\/9 - 28 t) - 1\/9 sin(20\/13 - 21 t) - 1\/11 sin(11\/7 - 19 t) - 1\/8 sin(20\/13 - 17 t) - 1\/24 sin(14\/9 - 15 t) - 1\/5 sin(14\/9 - 11 t) + 292\/13 sin(t + 11\/7) + 35\/4 sin(2 t + 19\/12) + 2\/7 sin(3 t + 18\/11) + 9\/10 sin(4 t + 19\/12) + 5\/7 sin(5 t + 8\/5) + 3\/4 sin(6 t + 8\/5) + 1\/40 sin(7 t + 47\/10) + 1\/5 sin(8 t + 11\/7) + 2\/5 sin(9 t + 8\/5) + 1\/9 sin(10 t + 8\/5) + 3\/8 sin(12 t + 13\/8) + 1\/34 sin(13 t + 13\/8) + 1\/29 sin(14 t + 10\/7) + 1\/4 sin(16 t + 13\/8) + 1\/6 sin(18 t + 13\/8) + 2\/13 sin(20 t + 13\/8) + 1\/9 sin(22 t + 8\/5) + 1\/29 sin(23 t + 47\/10) + 1\/14 sin(24 t + 18\/11) + 1\/76 sin(25 t + 51\/11) + 1\/16 sin(27 t + 17\/10) + 1\/14 sin(29 t + 5\/3) - 306\/13) theta(59 pi - t) theta(t - 55 pi) + (-1\/17 sin(11\/7 - 19 t) - 1\/44 sin(29\/19 - 16 t) - 1\/9 sin(17\/11 - 15 t) - 1\/23 sin(17\/11 - 14 t) - 1\/10 sin(14\/9 - 13 t) - 2\/9 sin(14\/9 - 11 t) - 3\/13 sin(17\/11 - 10 t) - 1\/3 sin(14\/9 - 9 t) - 1\/32 sin(3\/2 - 8 t) - 3\/13 sin(11\/7 - 7 t) - 4\/5 sin(11\/7 - 5 t) - 16\/31 sin(14\/9 - 3 t) - 81\/5 sin(11\/7 - t) + 31\/11 sin(2 t + 11\/7) + 2\/5 sin(4 t + 11\/7) + 1\/21 sin(6 t + 32\/21) + 1\/41 sin(17 t + 47\/10) + 1\/77 sin(21 t + 14\/3) + 1\/14 sin(22 t + 8\/5) + 1\/23 sin(23 t + 13\/8) + 1\/28 sin(24 t + 19\/12) + 1\/75 sin(25 t + 37\/8) + 1\/54 sin(27 t + 18\/11) + 1\/18 sin(28 t + 13\/8) - 213\/10) theta(55 pi - t) theta(t - 51 pi) + (-1\/52 sin(28\/27 - 29 t) - 1\/11 sin(22\/15 - 28 t) - 1\/81 sin(11\/12 - 27 t) - 1\/9 sin(3\/2 - 26 t) - 1\/10 sin(35\/23 - 24 t) - 1\/7 sin(3\/2 - 22 t) - 1\/93 sin(1 - 21 t) - 1\/9 sin(26\/17 - 20 t) - 1\/40 sin(10\/9 - 19 t) - 1\/9 sin(16\/11 - 18 t) - 1\/4 sin(17\/11 - 16 t) - 1\/16 sin(4\/3 - 15 t) - 4\/13 sin(35\/23 - 14 t) - 1\/10 sin(11\/8 - 13 t) - 2\/7 sin(17\/11 - 12 t) - 1\/19 sin(18\/13 - 11 t) - 1\/3 sin(17\/11 - 10 t) - 2\/9 sin(3\/2 - 9 t) - 3\/4 sin(17\/11 - 8 t) - 3\/2 sin(14\/9 - 6 t) - 13\/11 sin(26\/17 - 5 t) - 13\/3 sin(14\/9 - 4 t) - 6\/7 sin(20\/13 - 3 t) + 723\/19 sin(t + 11\/7) + 67\/9 sin(2 t + 33\/7) + 2\/11 sin(7 t + 20\/13) + 1\/95 sin(23 t + 3\/8) + 1\/41 sin(25 t + 25\/19) + 263\/5) theta(51 pi - t) theta(t - 47 pi) + (-1\/15 sin(17\/12 - 20 t) - 3\/11 sin(14\/9 - 18 t) - 1\/8 sin(20\/13 - 14 t) - 5\/6 sin(11\/7 - 7 t) + 676\/27 sin(t + 33\/7) + 78\/11 sin(2 t + 33\/7) + 135\/34 sin(3 t + 33\/7) + 15\/8 sin(4 t + 11\/7) + 37\/10 sin(5 t + 33\/7) + 3\/8 sin(6 t + 11\/7) + 3\/8 sin(8 t + 75\/16) + 5\/7 sin(9 t + 14\/9) + 3\/2 sin(10 t + 47\/10) + 1\/2 sin(11 t + 11\/7) + 3\/13 sin(12 t + 26\/17) + 2\/3 sin(13 t + 75\/16) + 7\/13 sin(15 t + 11\/7) + 2\/3 sin(16 t + 47\/10) + 3\/11 sin(17 t + 11\/7) + 1\/7 sin(19 t + 13\/8) + 1\/18 sin(21 t + 95\/21) + 1\/4 sin(22 t + 33\/7) + 1\/3 sin(23 t + 14\/9) + 1\/6 sin(24 t + 47\/10) + 1\/5 sin(25 t + 14\/3) + 1\/21 sin(26 t + 11\/7) + 1\/5 sin(27 t + 26\/17) + 2\/7 sin(28 t + 61\/13) + 1\/64 sin(29 t + 23\/5) + 379\/9) theta(47 pi - t) theta(t - 43 pi) + (-1\/9 sin(14\/9 - 24 t) - 1\/9 sin(34\/23 - 21 t) - 1\/4 sin(20\/13 - 20 t) - 1\/9 sin(13\/9 - 19 t) - 1\/37 sin(6\/5 - 18 t) - 1\/25 sin(10\/7 - 17 t) - 1\/8 sin(3\/2 - 15 t) - 7\/20 sin(23\/15 - 14 t) - 8\/11 sin(14\/9 - 13 t) - 13\/8 sin(11\/7 - 9 t) - 9\/11 sin(14\/9 - 8 t) - 5\/14 sin(26\/17 - 7 t) - 1\/5 sin(23\/17 - 5 t) - 20\/11 sin(20\/13 - 4 t) - 45\/8 sin(14\/9 - 3 t) - 69\/4 sin(11\/7 - 2 t) + 261\/13 sin(t + 11\/7) + 5\/7 sin(6 t + 14\/9) + 1\/9 sin(10 t + 11\/8) + 1\/7 sin(11 t + 4\/3) + 1\/7 sin(12 t + 17\/12) + 1\/41 sin(16 t + 7\/5) + 1\/11 sin(22 t + 35\/23) + 1\/20 sin(23 t + 17\/11) + 509\/14) theta(43 pi - t) theta(t - 39 pi) + (-1\/39 sin(14\/9 - 8 t) - 1\/47 sin(14\/9 - 7 t) - 1\/25 sin(11\/7 - 6 t) - 12\/25 sin(11\/7 - 2 t) - 1\/2 sin(11\/7 - t) + 4\/7 sin(3 t + 11\/7) + 1\/10 sin(4 t + 33\/7) + 1\/52 sin(5 t + 14\/9) + 1\/20 sin(9 t + 19\/12) - 141\/10) theta(39 pi - t) theta(t - 35 pi) + (-1\/12 sin(11\/7 - 5 t) + sin(t + 33\/7) + 14\/13 sin(2 t + 11\/7) + 3\/11 sin(3 t + 11\/7) + 1\/6 sin(4 t + 11\/7) + 1\/48 sin(6 t + 11\/7) + 1\/84 sin(7 t + 8\/5) + 1\/13 sin(8 t + 11\/7) - 114\/7) theta(35 pi - t) theta(t - 31 pi) + (7\/9 sin(t + 33\/7) + 16\/7 sin(2 t + 11\/7) + 1\/5 sin(3 t + 11\/7) + 2\/5 sin(4 t + 33\/7) + 1\/24 sin(5 t + 11\/7) + 1\/8 sin(6 t + 11\/7) - 37\/10) theta(31 pi - t) theta(t - 27 pi) + (-1\/29 sin(11\/7 - 25 t) - 1\/33 sin(14\/9 - 22 t) - 1\/26 sin(11\/7 - 16 t) - 1\/24 sin(14\/9 - 15 t) - 1\/21 sin(14\/9 - 9 t) + 112\/11 sin(t + 11\/7) + 12\/5 sin(2 t + 11\/7) + 8\/7 sin(3 t + 11\/7) + 8\/15 sin(4 t + 11\/7) + 1\/5 sin(5 t + 11\/7) + 1\/12 sin(6 t + 19\/12) + 5\/12 sin(8 t + 11\/7) + 2\/11 sin(11 t + 11\/7) + 1\/9 sin(12 t + 33\/7) + 1\/7 sin(13 t + 19\/12) + 1\/7 sin(14 t + 11\/7) + 1\/12 sin(18 t + 19\/12) + 1\/69 sin(19 t + 19\/12) + 1\/30 sin(21 t + 14\/9) + 1\/14 sin(23 t + 19\/12) + 1\/23 sin(24 t + 14\/9) - 19\/2) theta(27 pi - t) theta(t - 23 pi) + (-1\/24 sin(14\/9 - 8 t) - 1\/27 sin(11\/7 - 6 t) - 1\/8 sin(14\/9 - 4 t) - 1\/8 sin(11\/7 - 3 t) - 6\/7 sin(11\/7 - t) + 13\/11 sin(2 t + 11\/7) + 1\/8 sin(5 t + 11\/7) + 1\/16 sin(7 t + 19\/12) - 349\/13) theta(23 pi - t) theta(t - 19 pi) + (-1\/16 sin(14\/9 - 29 t) - 1\/56 sin(11\/8 - 28 t) - 1\/19 sin(17\/11 - 22 t) - 3\/10 sin(14\/9 - 19 t) - 1\/10 sin(17\/11 - 16 t) - 1\/5 sin(11\/7 - 13 t) - 1\/7 sin(11\/7 - 8 t) - 6\/7 sin(11\/7 - 7 t) - 15\/14 sin(14\/9 - 5 t) - 9\/4 sin(11\/7 - 3 t) - 37\/7 sin(11\/7 - t) + 5\/2 sin(2 t + 11\/7) + 3\/2 sin(4 t + 11\/7) + 2\/5 sin(6 t + 19\/12) + 1\/7 sin(9 t + 11\/7) + 3\/7 sin(10 t + 11\/7) + 1\/8 sin(11 t + 11\/7) + 1\/6 sin(12 t + 14\/9) + 2\/7 sin(14 t + 11\/7) + 1\/14 sin(15 t + 8\/5) + 1\/75 sin(18 t + 24\/13) + 1\/13 sin(20 t + 5\/3) + 1\/39 sin(21 t + 17\/11) + 1\/94 sin(23 t + 23\/14) + 1\/17 sin(24 t + 11\/7) + 1\/14 sin(25 t + 33\/7) + 1\/11 sin(26 t + 20\/13) + 1\/8 sin(27 t + 8\/5) - 1070\/51) theta(19 pi - t) theta(t - 15 pi) + (-1\/18 sin(29\/19 - 16 t) - 4\/3 sin(14\/9 - 8 t) + 89\/45 sin(t + 33\/7) + 12\/25 sin(2 t + 11\/7) + 1\/8 sin(3 t + 14\/9) + 1\/2 sin(4 t + 11\/7) + 3\/10 sin(5 t + 14\/9) + 4\/13 sin(6 t + 8\/5) + 1\/49 sin(7 t + 17\/8) + 7\/11 sin(9 t + 8\/5) + 5\/11 sin(10 t + 11\/7) + 1\/5 sin(11 t + 35\/23) + 1\/8 sin(12 t + 14\/9) + 1\/9 sin(13 t + 11\/7) + 1\/52 sin(14 t + 7\/4) + 1\/38 sin(15 t + 14\/3) + 2\/11 sin(17 t + 11\/7) + 1\/8 sin(18 t + 11\/7) + 1\/11 sin(19 t + 3\/2) + 1\/8 sin(20 t + 11\/7) + 1\/16 sin(21 t + 11\/7) + 1\/60 sin(22 t + 13\/8) + 1\/34 sin(24 t + 3\/2) + 1\/8 sin(25 t + 19\/12) + 1\/26 sin(26 t + 31\/21) + 1\/23 sin(27 t + 17\/11) + 1\/58 sin(28 t + 8\/5) + 1\/26 sin(29 t + 18\/11) + 1\/42 sin(30 t + 32\/21) - 392\/9) theta(15 pi - t) theta(t - 11 pi) + (-1\/34 sin(17\/11 - 19 t) - 1\/7 sin(34\/23 - 15 t) - 1\/7 sin(19\/13 - 14 t) - 1\/10 sin(22\/15 - 13 t) - 1\/18 sin(3\/2 - 11 t) - 1\/13 sin(10\/7 - 10 t) - 7\/20 sin(23\/15 - 9 t) - 1\/20 sin(23\/17 - 8 t) - 1\/7 sin(23\/15 - 7 t) - 10\/13 sin(14\/9 - 5 t) - 3\/11 sin(11\/7 - 3 t) - 232\/17 sin(11\/7 - t) + 47\/14 sin(2 t + 11\/7) + 2\/7 sin(4 t + 14\/9) + 1\/19 sin(6 t + 17\/12) + 1\/11 sin(12 t + 35\/23) + 1\/46 sin(17 t + 5\/3) + 1\/28 sin(18 t + 8\/5) - 325\/11) theta(11 pi - t) theta(t - 7 pi) + (-1\/22 sin(7\/5 - 37 t) - 1\/35 sin(14\/9 - 32 t) - 1\/6 sin(14\/9 - 27 t) - 1\/5 sin(29\/19 - 22 t) - 2\/5 sin(11\/7 - 20 t) - 1\/8 sin(11\/7 - 16 t) - 1\/11 sin(11\/8 - 15 t) - 1\/5 sin(26\/17 - 13 t) - 3\/13 sin(28\/19 - 12 t) - 85\/12 sin(11\/7 - 5 t) - 4 sin(11\/7 - 3 t) + 140\/9 sin(t + 33\/7) + 322\/15 sin(2 t + 33\/7) + 111\/17 sin(4 t + 11\/7) + 7\/9 sin(6 t + 8\/5) + sin(7 t + 11\/7) + 14\/13 sin(8 t + 14\/9) + 4\/5 sin(9 t + 75\/16) + 51\/26 sin(10 t + 47\/10) + 8\/13 sin(11 t + 21\/13) + 1\/17 sin(14 t + 18\/11) + 4\/11 sin(17 t + 37\/8) + 1\/16 sin(18 t + 19\/11) + 3\/10 sin(19 t + 11\/7) + 3\/13 sin(21 t + 5\/3) + 1\/15 sin(23 t + 10\/7) + 1\/4 sin(24 t + 14\/3) + 1\/9 sin(25 t + 14\/3) + 1\/6 sin(26 t + 17\/11) + 1\/12 sin(28 t + 7\/4) + 1\/6 sin(29 t + 47\/10) + 1\/34 sin(31 t + 14\/3) + 1\/16 sin(33 t + 10\/7) + 1\/22 sin(34 t + 33\/7) + 1\/10 sin(35 t + 32\/7) + 1\/14 sin(38 t + 19\/12) + 49\/24) theta(7 pi - t) theta(t - 3 pi) + (-1\/61 sin(7\/13 - 19 t) - 1\/24 sin(25\/19 - 15 t) - 1\/8 sin(9\/7 - 14 t) - 1\/5 sin(16\/11 - 8 t) - 41\/7 sin(2\/11 - t) + 33\/32 sin(2 t + 20\/13) + 21\/13 sin(3 t + 8\/13) + 4\/5 sin(4 t + 47\/10) + 5\/6 sin(5 t + 11\/3) + 2\/9 sin(6 t + 1) + 2\/5 sin(7 t + 23\/17) + 1\/8 sin(9 t + 7\/6) + 1\/8 sin(10 t + 8\/3) + 1\/14 sin(11 t + 5\/6) + 1\/50 sin(12 t + 11\/9) + 1\/7 sin(13 t + 9\/11) + 1\/11 sin(16 t + 53\/18) + 1\/18 sin(17 t + 7\/6) + 1\/35 sin(18 t + 61\/14) + 1\/15 sin(20 t + 73\/21) + 141\/20) theta(3 pi - t) theta(t + pi)) theta(sqrt(sgn(sin(t\/2))))


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