Trigonometric Functions

Analysis and thinking about trigonometry functions and how they work.

Sine

\begin{equation}
  sine \left(radian\right) = 
  \sum_{current=0}^{maximum}{
    -1 ^ i  \times
    \frac{
      radian ^ {\left( 2\times current +1 \right)}
    }{
      \left( 2 \times current + 1 \right) !
    }
  }
\end{equation}

Maximum

maximum = 1

Degree	Response	Expected response	Correct answer
0	0	0	[x]
20	0.349066	0.342020143	[ ]
45	0.875398	0.707106781	[ ]
80	1.39626	0.984807753	[ ]
90	1.5708	1	[ ]
120	2.0944	0.866025404	[ ]
180	3.14159	0	[ ]
270	4.71239	−1	[ ]
360	0	0	[x]

maximum = 7

Degree	Response	Expected response	Correct answer
0	0	0	[x]
20	0.34202	0.342020143	[x]
45	0.707107	0.707106781	[x]
80	0.984808	0.984807753	[x]
90	1	1	[x]
120	0.866031	0.866025404	[x]
180	0.00105761	0	[ ]
270	-0.789398	−1	[ ]
360	0	0	[x]

maximum = 15

Degree	Response	Expected response	Correct answer
0	0	0	[x]
20	0.34202	0.342020143	[x]
45	0.707107	0.707106781	[x]
80	0.984782	0.984807753	[x]
90	0.999408	1	[ ]
120	-1.08921	0.866025404	[ ]
180	-227481	0	[ ]
270	-2.79025e+010	−1	[ ]
360	0	0	[x]

maximum = 17

Degree	Response	Expected response	Correct answer
0	0	0	[x]
20	0.34202	0.342020143	[x]
45	0.707107	0.707106781	[x]
80	0.984711	0.984807753	[x]
90	0.9964	1	[ ]
120	-31.5645	0.866025404	[ ]
180	-1.55808e+007	0	[ ]
270	-8.70732e+012	−1	[ ]
360	0	0	[x]

maximum = 20

Degree	Response	Expected response	Correct answer
0	0	0	[x]
20	0.34202	0.342020143	[x]
45	0.707107	0.707106781	[x]
80	0.984808	0.984807753	[x]
90	1	1	[x]
120	0.866025	0.866025404	[x]
180	-5.28918e-010	0	[ ]
270	-1	−1	[x]
360	0	0	[x]

maximum = 40

Degree	Response	Expected response	Correct answer
0	0	0	[x]
20	0.34202	0.342020143	[x]
45	0.707107	0.707106781	[x]
80	0.984808	0.984807753	[x]
90	1	1	[x]
120	0.866025	0.866025404	[x]
180	3.32806e-016	0	[ ]
270	-1	−1	[x]
360	0	0	[x]

Cosine

\begin{equation}
  cosine \left(radian\right) = 
  \sum_{current=0}^{maximum}{
    -1 ^ i  \times
    \frac{
      radian ^ {\left( 2\times current \right)}
    }{
      \left( 2 \times current \right) !
    }
  }
\end{equation}

Tangent

\begin{equation}
  tangent\left(radian\right) = 
  \sum_{current=0}^{maximum}{
    -1 ^ i  \times
    \frac{
      \frac{
        radian ^ {\left( 2\times current \right)}
      }{
        \left( 2 \times current \right) !
      }
    }{
      \frac{
        radian ^ {\left( 2\times current +1 \right)}
      }{
        \left( 2 \times current + 1 \right) !
      }
    }
  }
\end{equation}

Cotangent

\begin{equation}
  cotangent \left(radian\right) = 
  \sum_{current=0}^{maximum}{
    -1 ^ i  \times
    \frac{
      \frac{
        radian ^ {\left( 2\times current +1 \right)}
      }{
        \left( 2 \times current + 1 \right) !
      }
    }{
      \frac{
        radian ^ {\left( 2\times current \right)}
      }{
        \left( 2 \times current \right) !
      }
    }
  }
\end{equation}

Relationships and Converters

The source of this image is Wikipedia.

\begin{equation}
	cosine \left( - A \right) = 
	cosine \left( A\right)
\end{equation}

\begin{equation}
	sine \left( - A \right) = 
	- sine \left( A\right)
\end{equation}

\begin{equation}
	cotangent \left(A \right) = 
	tangent \left( \frac{\pi}{2}  - A\right)
\end{equation}

\begin{equation}
	secant \left(A \right) = 
	cosecant \left( \frac{\pi}{2}  - A\right)
\end{equation}

\begin{equation}
	cosecant \left(A \right) = 
	secant \left( \frac{\pi}{2}  - A\right)
\end{equation}

\begin{equation}
	tan \left(A \right) = 
	cot \left( \frac{\pi}{2}  - A\right)
\end{equation}

Check Result

An example of conversion and analysis algorithms

> 0 degree

sin(0) = sin(0) = 0

> 1 degree

sin(1) = sin(1) = 0.0174524

> 2 degree

sin(2) = sin(2) = 0.0348995

> 3 degree

sin(3) = sin(3) = 0.052336

> 4 degree

sin(4) = sin(4) = 0.0697565

> 5 degree

sin(5) = sin(5) = 0.0871557

> 6 degree

sin(6) = sin(6) = 0.104528

> 7 degree

sin(7) = sin(7) = 0.121869

> 8 degree

sin(8) = sin(8) = 0.139173

> 9 degree

sin(9) = sin(9) = 0.156434

> 10 degree

sin(10) = sin(10) = 0.173648

> 11 degree

sin(11) = sin(11) = 0.190809

> 12 degree

sin(12) = sin(12) = 0.207912

> 13 degree

sin(13) = sin(13) = 0.224951

> 14 degree

sin(14) = sin(14) = 0.241922

> 15 degree

sin(15) = sin(15) = 0.258819

> 16 degree

sin(16) = sin(16) = 0.275637

> 17 degree

sin(17) = sin(17) = 0.292372

> 18 degree

sin(18) = sin(18) = 0.309017

> 19 degree

sin(19) = sin(19) = 0.325568

> 20 degree

sin(20) = sin(20) = 0.34202

> 21 degree

sin(21) = sin(21) = 0.358368

> 22 degree

sin(22) = sin(22) = 0.374607

> 23 degree

sin(23) = sin(23) = 0.390731

> 24 degree

sin(24) = sin(24) = 0.406737

> 25 degree

sin(25) = sin(25) = 0.422618

> 26 degree

sin(26) = sin(26) = 0.438371

> 27 degree

sin(27) = sin(27) = 0.45399

> 28 degree

sin(28) = sin(28) = 0.469472

> 29 degree

sin(29) = sin(29) = 0.48481

> 30 degree

sin(30) = sin(30) = 0.5

> 31 degree

sin(31) = sin(31) = 0.515038

> 32 degree

sin(32) = sin(32) = 0.529919

> 33 degree

sin(33) = sin(33) = 0.544639

> 34 degree

sin(34) = sin(34) = 0.559193

> 35 degree

sin(35) = sin(35) = 0.573576

> 36 degree

sin(36) = sin(36) = 0.587785

> 37 degree

sin(37) = sin(37) = 0.601815

> 38 degree

sin(38) = sin(38) = 0.615661

> 39 degree

sin(39) = sin(39) = 0.62932

> 40 degree

sin(40) = sin(40) = 0.642788

> 41 degree

sin(41) = sin(41) = 0.656059

> 42 degree

sin(42) = sin(42) = 0.669131

> 43 degree

sin(43) = sin(43) = 0.681998

> 44 degree

sin(44) = sin(44) = 0.694658

> 45 degree

sin(45) = sin(45) = 0.707107

> 46 degree

sin(46) = sin(46) = 0.71934

> 47 degree

sin(47) = sin(47) = 0.731354

> 48 degree

sin(48) = sin(48) = 0.743145

> 49 degree

sin(49) = sin(49) = 0.75471

> 50 degree

sin(50) = sin(50) = 0.766044

> 51 degree

sin(51) = sin(51) = 0.777146

> 52 degree

sin(52) = sin(52) = 0.788011

> 53 degree

sin(53) = sin(53) = 0.798636

> 54 degree

sin(54) = sin(54) = 0.809017

> 55 degree

sin(55) = sin(55) = 0.819152

> 56 degree

sin(56) = sin(56) = 0.829038

> 57 degree

sin(57) = sin(57) = 0.838671

> 58 degree

sin(58) = sin(58) = 0.848048

> 59 degree

sin(59) = sin(59) = 0.857167

> 60 degree

sin(60) = sin(60) = 0.866025

> 61 degree

sin(61) = sin(61) = 0.87462

> 62 degree

sin(62) = sin(62) = 0.882948

> 63 degree

sin(63) = sin(63) = 0.891007

> 64 degree

sin(64) = sin(64) = 0.898794

> 65 degree

sin(65) = sin(65) = 0.906308

> 66 degree

sin(66) = sin(66) = 0.913545

> 67 degree

sin(67) = sin(67) = 0.920505

> 68 degree

sin(68) = sin(68) = 0.927184

> 69 degree

sin(69) = sin(69) = 0.93358

> 70 degree

sin(70) = sin(70) = 0.939693

> 71 degree

sin(71) = sin(71) = 0.945519

> 72 degree

sin(72) = sin(72) = 0.951057

> 73 degree

sin(73) = sin(73) = 0.956305

> 74 degree

sin(74) = sin(74) = 0.961262

> 75 degree

sin(75) = sin(75) = 0.965926

> 76 degree

sin(76) = sin(76) = 0.970296

> 77 degree

sin(77) = sin(77) = 0.97437

> 78 degree

sin(78) = sin(78) = 0.978148

> 79 degree

sin(79) = sin(79) = 0.981627

> 80 degree

sin(80) = sin(80) = 0.984808

> 81 degree

sin(81) = sin(81) = 0.987688

> 82 degree

sin(82) = sin(82) = 0.990268

> 83 degree

sin(83) = sin(83) = 0.992546

> 84 degree

sin(84) = sin(84) = 0.994522

> 85 degree

sin(85) = sin(85) = 0.996195

> 86 degree

sin(86) = sin(86) = 0.997564

> 87 degree

sin(87) = sin(87) = 0.99863

> 88 degree

sin(88) = sin(88) = 0.999391

> 89 degree

sin(89) = sin(89) = 0.999848

> 90 degree

sin(90) = cos(0) = 1

> 91 degree

sin(91) = cos(1) = 0.999848

> 92 degree

sin(92) = cos(2) = 0.999391

> 93 degree

sin(93) = cos(3) = 0.99863

> 94 degree

sin(94) = cos(4) = 0.997564

> 95 degree

sin(95) = cos(5) = 0.996195

> 96 degree

sin(96) = cos(6) = 0.994522

> 97 degree

sin(97) = cos(7) = 0.992546

> 98 degree

sin(98) = cos(8) = 0.990268

> 99 degree

sin(99) = cos(9) = 0.987688

> 100 degree

sin(100) = cos(10) = 0.984808

> 101 degree

sin(101) = cos(11) = 0.981627

> 102 degree

sin(102) = cos(12) = 0.978148

> 103 degree

sin(103) = cos(13) = 0.97437

> 104 degree

sin(104) = cos(14) = 0.970296

> 105 degree

sin(105) = cos(15) = 0.965926

> 106 degree

sin(106) = cos(16) = 0.961262

> 107 degree

sin(107) = cos(17) = 0.956305

> 108 degree

sin(108) = cos(18) = 0.951057

> 109 degree

sin(109) = cos(19) = 0.945519

> 110 degree

sin(110) = cos(20) = 0.939693

> 111 degree

sin(111) = cos(21) = 0.93358

> 112 degree

sin(112) = cos(22) = 0.927184

> 113 degree

sin(113) = cos(23) = 0.920505

> 114 degree

sin(114) = cos(24) = 0.913545

> 115 degree

sin(115) = cos(25) = 0.906308

> 116 degree

sin(116) = cos(26) = 0.898794

> 117 degree

sin(117) = cos(27) = 0.891007

> 118 degree

sin(118) = cos(28) = 0.882948

> 119 degree

sin(119) = cos(29) = 0.87462

> 120 degree

sin(120) = cos(30) = 0.866025

> 121 degree

sin(121) = cos(31) = 0.857167

> 122 degree

sin(122) = cos(32) = 0.848048

> 123 degree

sin(123) = cos(33) = 0.838671

> 124 degree

sin(124) = cos(34) = 0.829038

> 125 degree

sin(125) = cos(35) = 0.819152

> 126 degree

sin(126) = cos(36) = 0.809017

> 127 degree

sin(127) = cos(37) = 0.798636

> 128 degree

sin(128) = cos(38) = 0.788011

> 129 degree

sin(129) = cos(39) = 0.777146

> 130 degree

sin(130) = cos(40) = 0.766044

> 131 degree

sin(131) = cos(41) = 0.75471

> 132 degree

sin(132) = cos(42) = 0.743145

> 133 degree

sin(133) = cos(43) = 0.731354

> 134 degree

sin(134) = cos(44) = 0.71934

> 135 degree

sin(135) = cos(45) = 0.707107

> 136 degree

sin(136) = cos(46) = 0.694658

> 137 degree

sin(137) = cos(47) = 0.681998

> 138 degree

sin(138) = cos(48) = 0.669131

> 139 degree

sin(139) = cos(49) = 0.656059

> 140 degree

sin(140) = cos(50) = 0.642788

> 141 degree

sin(141) = cos(51) = 0.62932

> 142 degree

sin(142) = cos(52) = 0.615661

> 143 degree

sin(143) = cos(53) = 0.601815

> 144 degree

sin(144) = cos(54) = 0.587785

> 145 degree

sin(145) = cos(55) = 0.573576

> 146 degree

sin(146) = cos(56) = 0.559193

> 147 degree

sin(147) = cos(57) = 0.544639

> 148 degree

sin(148) = cos(58) = 0.529919

> 149 degree

sin(149) = cos(59) = 0.515038

> 150 degree

sin(150) = cos(60) = 0.5

> 151 degree

sin(151) = cos(61) = 0.48481

> 152 degree

sin(152) = cos(62) = 0.469472

> 153 degree

sin(153) = cos(63) = 0.45399

> 154 degree

sin(154) = cos(64) = 0.438371

> 155 degree

sin(155) = cos(65) = 0.422618

> 156 degree

sin(156) = cos(66) = 0.406737

> 157 degree

sin(157) = cos(67) = 0.390731

> 158 degree

sin(158) = cos(68) = 0.374607

> 159 degree

sin(159) = cos(69) = 0.358368

> 160 degree

sin(160) = cos(70) = 0.34202

> 161 degree

sin(161) = cos(71) = 0.325568

> 162 degree

sin(162) = cos(72) = 0.309017

> 163 degree

sin(163) = cos(73) = 0.292372

> 164 degree

sin(164) = cos(74) = 0.275637

> 165 degree

sin(165) = cos(75) = 0.258819

> 166 degree

sin(166) = cos(76) = 0.241922

> 167 degree

sin(167) = cos(77) = 0.224951

> 168 degree

sin(168) = cos(78) = 0.207912

> 169 degree

sin(169) = cos(79) = 0.190809

> 170 degree

sin(170) = cos(80) = 0.173648

> 171 degree

sin(171) = cos(81) = 0.156434

> 172 degree

sin(172) = cos(82) = 0.139173

> 173 degree

sin(173) = cos(83) = 0.121869

> 174 degree

sin(174) = cos(84) = 0.104528

> 175 degree

sin(175) = cos(85) = 0.0871557

> 176 degree

sin(176) = cos(86) = 0.0697565

> 177 degree

sin(177) = cos(87) = 0.052336

> 178 degree

sin(178) = cos(88) = 0.0348995

> 179 degree

sin(179) = cos(89) = 0.0174524

> 180 degree

sin(180) = -sin(0) = -0

> 181 degree

sin(181) = -sin(1) = -0.0174524

> 182 degree

sin(182) = -sin(2) = -0.0348995

> 183 degree

sin(183) = -sin(3) = -0.052336

> 184 degree

sin(184) = -sin(4) = -0.0697565

> 185 degree

sin(185) = -sin(5) = -0.0871557

> 186 degree

sin(186) = -sin(6) = -0.104528

> 187 degree

sin(187) = -sin(7) = -0.121869

> 188 degree

sin(188) = -sin(8) = -0.139173

> 189 degree

sin(189) = -sin(9) = -0.156434

> 190 degree

sin(190) = -sin(10) = -0.173648

> 191 degree

sin(191) = -sin(11) = -0.190809

> 192 degree

sin(192) = -sin(12) = -0.207912

> 193 degree

sin(193) = -sin(13) = -0.224951

> 194 degree

sin(194) = -sin(14) = -0.241922

> 195 degree

sin(195) = -sin(15) = -0.258819

> 196 degree

sin(196) = -sin(16) = -0.275637

> 197 degree

sin(197) = -sin(17) = -0.292372

> 198 degree

sin(198) = -sin(18) = -0.309017

> 199 degree

sin(199) = -sin(19) = -0.325568

> 200 degree

sin(200) = -sin(20) = -0.34202

> 201 degree

sin(201) = -sin(21) = -0.358368

> 202 degree

sin(202) = -sin(22) = -0.374607

> 203 degree

sin(203) = -sin(23) = -0.390731

> 204 degree

sin(204) = -sin(24) = -0.406737

> 205 degree

sin(205) = -sin(25) = -0.422618

> 206 degree

sin(206) = -sin(26) = -0.438371

> 207 degree

sin(207) = -sin(27) = -0.45399

> 208 degree

sin(208) = -sin(28) = -0.469472

> 209 degree

sin(209) = -sin(29) = -0.48481

> 210 degree

sin(210) = -sin(30) = -0.5

> 211 degree

sin(211) = -sin(31) = -0.515038

> 212 degree

sin(212) = -sin(32) = -0.529919

> 213 degree

sin(213) = -sin(33) = -0.544639

> 214 degree

sin(214) = -sin(34) = -0.559193

> 215 degree

sin(215) = -sin(35) = -0.573576

> 216 degree

sin(216) = -sin(36) = -0.587785

> 217 degree

sin(217) = -sin(37) = -0.601815

> 218 degree

sin(218) = -sin(38) = -0.615661

> 219 degree

sin(219) = -sin(39) = -0.62932

> 220 degree

sin(220) = -sin(40) = -0.642788

> 221 degree

sin(221) = -sin(41) = -0.656059

> 222 degree

sin(222) = -sin(42) = -0.669131

> 223 degree

sin(223) = -sin(43) = -0.681998

> 224 degree

sin(224) = -sin(44) = -0.694658

> 225 degree

sin(225) = -sin(45) = -0.707107

> 226 degree

sin(226) = -sin(46) = -0.71934

> 227 degree

sin(227) = -sin(47) = -0.731354

> 228 degree

sin(228) = -sin(48) = -0.743145

> 229 degree

sin(229) = -sin(49) = -0.75471

> 230 degree

sin(230) = -sin(50) = -0.766044

> 231 degree

sin(231) = -sin(51) = -0.777146

> 232 degree

sin(232) = -sin(52) = -0.788011

> 233 degree

sin(233) = -sin(53) = -0.798636

> 234 degree

sin(234) = -sin(54) = -0.809017

> 235 degree

sin(235) = -sin(55) = -0.819152

> 236 degree

sin(236) = -sin(56) = -0.829038

> 237 degree

sin(237) = -sin(57) = -0.838671

> 238 degree

sin(238) = -sin(58) = -0.848048

> 239 degree

sin(239) = -sin(59) = -0.857167

> 240 degree

sin(240) = -sin(60) = -0.866025

> 241 degree

sin(241) = -sin(61) = -0.87462

> 242 degree

sin(242) = -sin(62) = -0.882948

> 243 degree

sin(243) = -sin(63) = -0.891007

> 244 degree

sin(244) = -sin(64) = -0.898794

> 245 degree

sin(245) = -sin(65) = -0.906308

> 246 degree

sin(246) = -sin(66) = -0.913545

> 247 degree

sin(247) = -sin(67) = -0.920505

> 248 degree

sin(248) = -sin(68) = -0.927184

> 249 degree

sin(249) = -sin(69) = -0.93358

> 250 degree

sin(250) = -sin(70) = -0.939693

> 251 degree

sin(251) = -sin(71) = -0.945519

> 252 degree

sin(252) = -sin(72) = -0.951057

> 253 degree

sin(253) = -sin(73) = -0.956305

> 254 degree

sin(254) = -sin(74) = -0.961262

> 255 degree

sin(255) = -sin(75) = -0.965926

> 256 degree

sin(256) = -sin(76) = -0.970296

> 257 degree

sin(257) = -sin(77) = -0.97437

> 258 degree

sin(258) = -sin(78) = -0.978148

> 259 degree

sin(259) = -sin(79) = -0.981627

> 260 degree

sin(260) = -sin(80) = -0.984808

> 261 degree

sin(261) = -sin(81) = -0.987688

> 262 degree

sin(262) = -sin(82) = -0.990268

> 263 degree

sin(263) = -sin(83) = -0.992546

> 264 degree

sin(264) = -sin(84) = -0.994522

> 265 degree

sin(265) = -sin(85) = -0.996195

> 266 degree

sin(266) = -sin(86) = -0.997564

> 267 degree

sin(267) = -sin(87) = -0.99863

> 268 degree

sin(268) = -sin(88) = -0.999391

> 269 degree

sin(269) = -sin(89) = -0.999848

> 270 degree

sin(270) = -sin(90) = -1

> 271 degree

sin(271) = -sin(91) = -0.999848

> 272 degree

sin(272) = -sin(92) = -0.999391

> 273 degree

sin(273) = -sin(93) = -0.99863

> 274 degree

sin(274) = -sin(94) = -0.997564

> 275 degree

sin(275) = -sin(95) = -0.996195

> 276 degree

sin(276) = -sin(96) = -0.994522

> 277 degree

sin(277) = -sin(97) = -0.992546

> 278 degree

sin(278) = -sin(98) = -0.990268

> 279 degree

sin(279) = -sin(99) = -0.987688

> 280 degree

sin(280) = -sin(100) = -0.984808

> 281 degree

sin(281) = -sin(101) = -0.981627

> 282 degree

sin(282) = -sin(102) = -0.978148

> 283 degree

sin(283) = -sin(103) = -0.97437

> 284 degree

sin(284) = -sin(104) = -0.970296

> 285 degree

sin(285) = -sin(105) = -0.965926

> 286 degree

sin(286) = -sin(106) = -0.961262

> 287 degree

sin(287) = -sin(107) = -0.956305

> 288 degree

sin(288) = -sin(108) = -0.951057

> 289 degree

sin(289) = -sin(109) = -0.945519

> 290 degree

sin(290) = -sin(110) = -0.939693

> 291 degree

sin(291) = -sin(111) = -0.93358

> 292 degree

sin(292) = -sin(112) = -0.927184

> 293 degree

sin(293) = -sin(113) = -0.920505

> 294 degree

sin(294) = -sin(114) = -0.913545

> 295 degree

sin(295) = -sin(115) = -0.906308

> 296 degree

sin(296) = -sin(116) = -0.898794

> 297 degree

sin(297) = -sin(117) = -0.891007

> 298 degree

sin(298) = -sin(118) = -0.882948

> 299 degree

sin(299) = -sin(119) = -0.87462

> 300 degree

sin(300) = -sin(120) = -0.866025

> 301 degree

sin(301) = -sin(121) = -0.857167

> 302 degree

sin(302) = -sin(122) = -0.848048

> 303 degree

sin(303) = -sin(123) = -0.838671

> 304 degree

sin(304) = -sin(124) = -0.829038

> 305 degree

sin(305) = -sin(125) = -0.819152

> 306 degree

sin(306) = -sin(126) = -0.809017

> 307 degree

sin(307) = -sin(127) = -0.798636

> 308 degree

sin(308) = -sin(128) = -0.788011

> 309 degree

sin(309) = -sin(129) = -0.777146

> 310 degree

sin(310) = -sin(130) = -0.766044

> 311 degree

sin(311) = -sin(131) = -0.75471

> 312 degree

sin(312) = -sin(132) = -0.743145

> 313 degree

sin(313) = -sin(133) = -0.731354

> 314 degree

sin(314) = -sin(134) = -0.71934

> 315 degree

sin(315) = -sin(135) = -0.707107

> 316 degree

sin(316) = -sin(136) = -0.694658

> 317 degree

sin(317) = -sin(137) = -0.681998

> 318 degree

sin(318) = -sin(138) = -0.669131

> 319 degree

sin(319) = -sin(139) = -0.656059

> 320 degree

sin(320) = -sin(140) = -0.642788

> 321 degree

sin(321) = -sin(141) = -0.62932

> 322 degree

sin(322) = -sin(142) = -0.615661

> 323 degree

sin(323) = -sin(143) = -0.601815

> 324 degree

sin(324) = -sin(144) = -0.587785

> 325 degree

sin(325) = -sin(145) = -0.573576

> 326 degree

sin(326) = -sin(146) = -0.559193

> 327 degree

sin(327) = -sin(147) = -0.544639

> 328 degree

sin(328) = -sin(148) = -0.529919

> 329 degree

sin(329) = -sin(149) = -0.515038

> 330 degree

sin(330) = -sin(150) = -0.5

> 331 degree

sin(331) = -sin(151) = -0.48481

> 332 degree

sin(332) = -sin(152) = -0.469472

> 333 degree

sin(333) = -sin(153) = -0.45399

> 334 degree

sin(334) = -sin(154) = -0.438371

> 335 degree

sin(335) = -sin(155) = -0.422618

> 336 degree

sin(336) = -sin(156) = -0.406737

> 337 degree

sin(337) = -sin(157) = -0.390731

> 338 degree

sin(338) = -sin(158) = -0.374607

> 339 degree

sin(339) = -sin(159) = -0.358368

> 340 degree

sin(340) = -sin(160) = -0.34202

> 341 degree

sin(341) = -sin(161) = -0.325568

> 342 degree

sin(342) = -sin(162) = -0.309017

> 343 degree

sin(343) = -sin(163) = -0.292372

> 344 degree

sin(344) = -sin(164) = -0.275637

> 345 degree

sin(345) = -sin(165) = -0.258819

> 346 degree

sin(346) = -sin(166) = -0.241922

> 347 degree

sin(347) = -sin(167) = -0.224951

> 348 degree

sin(348) = -sin(168) = -0.207912

> 349 degree

sin(349) = -sin(169) = -0.190809

> 350 degree

sin(350) = -sin(170) = -0.173648

> 351 degree

sin(351) = -sin(171) = -0.156434

> 352 degree

sin(352) = -sin(172) = -0.139173

> 353 degree

sin(353) = -sin(173) = -0.121869

> 354 degree

sin(354) = -sin(174) = -0.104528

> 355 degree

sin(355) = -sin(175) = -0.0871557

> 356 degree

sin(356) = -sin(176) = -0.0697565

> 357 degree

sin(357) = -sin(177) = -0.052336

> 358 degree

sin(358) = -sin(178) = -0.0348995

> 359 degree

sin(359) = -sin(179) = -0.0174524

> 360 degree

sin(360) = sin(0) = 0

> 361 degree

sin(361) = sin(1) = 0.0174524

> 362 degree

sin(362) = sin(2) = 0.0348995

> 363 degree

sin(363) = sin(3) = 0.052336

> 364 degree

sin(364) = sin(4) = 0.0697565

> 365 degree

sin(365) = sin(5) = 0.0871557

> 366 degree

sin(366) = sin(6) = 0.104528

> 367 degree

sin(367) = sin(7) = 0.121869

> 368 degree

sin(368) = sin(8) = 0.139173

> 369 degree

sin(369) = sin(9) = 0.156434

> 370 degree

sin(370) = sin(10) = 0.173648

> 371 degree

sin(371) = sin(11) = 0.190809

> 372 degree

sin(372) = sin(12) = 0.207912

> 373 degree

sin(373) = sin(13) = 0.224951

> 374 degree

sin(374) = sin(14) = 0.241922

> 375 degree

sin(375) = sin(15) = 0.258819

> 376 degree

sin(376) = sin(16) = 0.275637

> 377 degree

sin(377) = sin(17) = 0.292372

> 378 degree

sin(378) = sin(18) = 0.309017

> 379 degree

sin(379) = sin(19) = 0.325568

> 380 degree

sin(380) = sin(20) = 0.34202

> 381 degree

sin(381) = sin(21) = 0.358368

> 382 degree

sin(382) = sin(22) = 0.374607

> 383 degree

sin(383) = sin(23) = 0.390731

> 384 degree

sin(384) = sin(24) = 0.406737

> 385 degree

sin(385) = sin(25) = 0.422618

> 386 degree

sin(386) = sin(26) = 0.438371

> 387 degree

sin(387) = sin(27) = 0.45399

> 388 degree

sin(388) = sin(28) = 0.469472

> 389 degree

sin(389) = sin(29) = 0.48481

> 390 degree

sin(390) = sin(30) = 0.5

> 391 degree

sin(391) = sin(31) = 0.515038

> 392 degree

sin(392) = sin(32) = 0.529919

> 393 degree

sin(393) = sin(33) = 0.544639

> 394 degree

sin(394) = sin(34) = 0.559193

> 395 degree

sin(395) = sin(35) = 0.573576

> 396 degree

sin(396) = sin(36) = 0.587785

> 397 degree

sin(397) = sin(37) = 0.601815

> 398 degree

sin(398) = sin(38) = 0.615661

> 399 degree

sin(399) = sin(39) = 0.62932

> 400 degree

sin(400) = sin(40) = 0.642788

> 401 degree

sin(401) = sin(41) = 0.656059

> 402 degree

sin(402) = sin(42) = 0.669131

> 403 degree

sin(403) = sin(43) = 0.681998

> 404 degree

sin(404) = sin(44) = 0.694658

> 405 degree

sin(405) = sin(45) = 0.707107

> 406 degree

sin(406) = sin(46) = 0.71934

> 407 degree

sin(407) = sin(47) = 0.731354

> 408 degree

sin(408) = sin(48) = 0.743145

> 409 degree

sin(409) = sin(49) = 0.75471

> 410 degree

sin(410) = sin(50) = 0.766044

> 411 degree

sin(411) = sin(51) = 0.777146

> 412 degree

sin(412) = sin(52) = 0.788011

> 413 degree

sin(413) = sin(53) = 0.798636

> 414 degree

sin(414) = sin(54) = 0.809017

> 415 degree

sin(415) = sin(55) = 0.819152

> 416 degree

sin(416) = sin(56) = 0.829038

> 417 degree

sin(417) = sin(57) = 0.838671

> 418 degree

sin(418) = sin(58) = 0.848048

> 419 degree

sin(419) = sin(59) = 0.857167

> 420 degree

sin(420) = sin(60) = 0.866025

> 421 degree

sin(421) = sin(61) = 0.87462

> 422 degree

sin(422) = sin(62) = 0.882948

> 423 degree

sin(423) = sin(63) = 0.891007

> 424 degree

sin(424) = sin(64) = 0.898794

> 425 degree

sin(425) = sin(65) = 0.906308

> 426 degree

sin(426) = sin(66) = 0.913545

> 427 degree

sin(427) = sin(67) = 0.920505

> 428 degree

sin(428) = sin(68) = 0.927184

> 429 degree

sin(429) = sin(69) = 0.93358

> 430 degree

sin(430) = sin(70) = 0.939693

> 431 degree

sin(431) = sin(71) = 0.945519

> 432 degree

sin(432) = sin(72) = 0.951057

> 433 degree

sin(433) = sin(73) = 0.956305

> 434 degree

sin(434) = sin(74) = 0.961262

> 435 degree

sin(435) = sin(75) = 0.965926

> 436 degree

sin(436) = sin(76) = 0.970296

> 437 degree

sin(437) = sin(77) = 0.97437

> 438 degree

sin(438) = sin(78) = 0.978148

> 439 degree

sin(439) = sin(79) = 0.981627

> 440 degree

sin(440) = sin(80) = 0.984808

> 441 degree

sin(441) = sin(81) = 0.987688

> 442 degree

sin(442) = sin(82) = 0.990268

> 443 degree

sin(443) = sin(83) = 0.992546

> 444 degree

sin(444) = sin(84) = 0.994522

> 445 degree

sin(445) = sin(85) = 0.996195

> 446 degree

sin(446) = sin(86) = 0.997564

> 447 degree

sin(447) = sin(87) = 0.99863

> 448 degree

sin(448) = sin(88) = 0.999391

> 449 degree

sin(449) = sin(89) = 0.999848

> 450 degree

sin(450) = sin(90) = 1

> 451 degree

sin(451) = sin(91) = 0.999848

> 452 degree

sin(452) = sin(92) = 0.999391

> 453 degree

sin(453) = sin(93) = 0.99863

> 454 degree

sin(454) = sin(94) = 0.997564

> 455 degree

sin(455) = sin(95) = 0.996195

> 456 degree

sin(456) = sin(96) = 0.994522

> 457 degree

sin(457) = sin(97) = 0.992546

> 458 degree

sin(458) = sin(98) = 0.990268

> 459 degree

sin(459) = sin(99) = 0.987688

> 460 degree

sin(460) = sin(100) = 0.984808

> 461 degree

sin(461) = sin(101) = 0.981627

> 462 degree

sin(462) = sin(102) = 0.978148

> 463 degree

sin(463) = sin(103) = 0.97437

> 464 degree

sin(464) = sin(104) = 0.970296

> 465 degree

sin(465) = sin(105) = 0.965926

> 466 degree

sin(466) = sin(106) = 0.961262

> 467 degree

sin(467) = sin(107) = 0.956305

> 468 degree

sin(468) = sin(108) = 0.951057

> 469 degree

sin(469) = sin(109) = 0.945519

> 470 degree

sin(470) = sin(110) = 0.939693

> 471 degree

sin(471) = sin(111) = 0.93358

> 472 degree

sin(472) = sin(112) = 0.927184

> 473 degree

sin(473) = sin(113) = 0.920505

> 474 degree

sin(474) = sin(114) = 0.913545

> 475 degree

sin(475) = sin(115) = 0.906308

> 476 degree

sin(476) = sin(116) = 0.898794

> 477 degree

sin(477) = sin(117) = 0.891007

> 478 degree

sin(478) = sin(118) = 0.882948

> 479 degree

sin(479) = sin(119) = 0.87462

> 480 degree

sin(480) = sin(120) = 0.866025

> 481 degree

sin(481) = sin(121) = 0.857167

> 482 degree

sin(482) = sin(122) = 0.848048

> 483 degree

sin(483) = sin(123) = 0.838671

> 484 degree

sin(484) = sin(124) = 0.829038

> 485 degree

sin(485) = sin(125) = 0.819152

> 486 degree

sin(486) = sin(126) = 0.809017

> 487 degree

sin(487) = sin(127) = 0.798636

> 488 degree

sin(488) = sin(128) = 0.788011

> 489 degree

sin(489) = sin(129) = 0.777146

> 490 degree

sin(490) = sin(130) = 0.766044

> 491 degree

sin(491) = sin(131) = 0.75471

> 492 degree

sin(492) = sin(132) = 0.743145

> 493 degree

sin(493) = sin(133) = 0.731354

> 494 degree

sin(494) = sin(134) = 0.71934

> 495 degree

sin(495) = sin(135) = 0.707107

> 496 degree

sin(496) = sin(136) = 0.694658

> 497 degree

sin(497) = sin(137) = 0.681998

> 498 degree

sin(498) = sin(138) = 0.669131

> 499 degree

sin(499) = sin(139) = 0.656059

The formulas picture created using Tex (xelatex) on the Unix System.

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