数学课上我们经常提到的正弦、余弦0度、90度、180度是什么?余弦从0到180,360有很多值。很多朋友想知道余弦 value 角度对照表的一些细节。以下是边肖编译的AND 余弦 value 角度对照表。
sin0 =0,cos 0 = 1;sin90 =1,cos 90 = 0;sin180 =0,cos180 =-1 .
结果分析
1.当角度为0时,角度两边重合,y轴上的值为0,所以sin0 = 0。
2.cosx=邻边/斜边。当x=0时,斜边和邻边相等,所以cos0 = 1。
3.sinα=r/y,其中r是单位圆的半径。当α=90度时,r=y,所以sin90度=1。
4.余弦是邻边与斜边的比值,90°直角的对边是长度为0的斜边,所以COS 90 = 0。
5.SIN 180 = SIN(90+90)= SIN 90 COS 90+COS 90 SIN 90 = 0,所以SIN 180 = 0。
6.设从180度角的终边上的一点P(x,0)到R的距离为R,则R =-X,根据三角函数的定义,COS 180 = X/R = X/(-X) =-1,所以COS 180 =-1。
1、平方和关系
(sinα)^2+(cosα)^2=1
2、产品之间的关系
Sinα=tanα×cosα(即sinα/cosα=tanα)
Cosα=cotα×sinα(即cosα/sinα=cotα)。
Tanα=sinα×secα(即tanα/sinα=secα)。
在三角形中,每条边与其对角线正弦的比值相等,即a/sinA=b/sinB=c/sinC。
S△ = c 2sinasinb/2sin (a+b) (s△是三角形的面积,三个角∠A∠B∠C,对边分别∠A,B,C)。
s△= 1/2 AC SINB = 1/2 BC SINA = 1/2 ABS Inc(三个角∠A∠B∠C,对边分别为A、B、C,见三角函数)。
另外,当sin值在180-360之间时,会出现负数,在360以上重复出现。
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
sec(2kπ+α)=secα
特殊角度的值如下:
在直角三角形中,任意锐角∠A的对边与斜边之比称为∠A的正弦,由英文单词sine缩写而来,即sinA = ∠ A的对边/斜边。
Sinα=tanα×cosα(即sinα/cosα=tanα)
Cosα=cotα×sinα(即cosα/sinα=cotα)。
Tanα=sinα×secα(即tanα/sinα=secα)。
sin(α β)=sinα cosβ cosα sinβ
sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγ
cos(α β)=cosαcosβsinβsinα
tan(α β)=(tanα tanβ)/(1tanαtanβ)
余弦值角度对照表0到360
cos(0 ) = 1
cos(1 ) = 0.999848
cos(2 ) = 0.999391
cos(3 ) = 0.99863
cos(4 ) = 0.997564
cos(5 ) = 0.996195
cos(6 ) = 0.994522
cos(7 ) = 0.992546
cos(8 ) = 0.990268
cos(9 ) = 0.987688
cos(10 ) = 0.984808
cos(11 ) = 0.981627
cos(12 ) = 0.978148
cos(13 ) = 0.97437
cos(14 ) = 0.970296
cos(15 ) = 0.965926
cos(16 ) = 0.961262
cos(17 ) = 0.956305
cos(18 ) = 0.951057
cos(19 ) = 0.945519
cos(20 ) = 0.939693
cos(21 ) = 0.93358
cos(22 ) = 0.927184
cos(23 ) = 0.920505
cos(24 ) = 0.913545
cos(25 ) = 0.906308
cos(26 ) = 0.898794
cos(27 ) = 0.891007
cos(28 ) = 0.882948
cos(29 ) = 0.87462
cos(30 ) = 0.866025
cos(31 ) = 0.857167
cos(32 ) = 0.848048
cos(33 ) = 0.838671
cos(34 ) = 0.829038
cos(35 ) = 0.819152
cos(36 ) = 0.809017
cos(37 ) = 0.798636
cos(38 ) = 0.788011
cos(39 ) = 0.777146
cos(40 ) = 0.766044
cos(41 ) = 0.75471
cos(42 ) = 0.743145
cos(43 ) = 0.731354
cos(44 ) = 0.71934
cos(45 ) = 0.707107
cos(46 ) = 0.694658
cos(47 ) = 0.681998
cos(48 ) = 0.669131
cos(49 ) = 0.656059
cos(50 ) = 0.642788
cos(51 ) = 0.62932
cos(52 ) = 0.615661
cos(53 ) = 0.601815
cos(54 ) = 0.587785
cos(55 ) = 0.573576
cos(56 ) = 0.559193
cos(57 ) = 0.544639
cos(58 ) = 0.529919
cos(59 ) = 0.515038
cos(60 ) = 0.5
cos(61 ) = 0.48481
cos(62 ) = 0.469472
cos(63 ) = 0.45399
cos(64 ) = 0.438371
cos(65 ) = 0.422618
cos(66 ) = 0.406737
cos(67 ) = 0.390731
cos(68 ) = 0.374607
cos(69 ) = 0.358368
cos(70 ) = 0.34202
cos(71 ) = 0.325568
cos(72 ) = 0.309017
cos(73 ) = 0.292372
cos(74 ) = 0.275637
cos(75 ) = 0.258819
cos(76 ) = 0.241922
cos(77 ) = 0.224951
cos(78 ) = 0.207912
cos(79 ) = 0.190809
cos(80 ) = 0.173648
cos(81 ) = 0.156434
cos(82 ) = 0.139173
cos(83 ) = 0.121869
cos(84 ) = 0.104528
cos(85 ) = 0.087156
cos(86 ) = 0.069756
cos(87 ) = 0.052336
cos(88 ) = 0.034899
cos(89 ) = 0.017452
cos(90 ) = 0
cos(91 ) = -0.017452
cos(92 ) = -0.034899
cos(93 ) = -0.052336
cos(94 ) = -0.069756
cos(95 ) = -0.087156
cos(96 ) = -0.104528
cos(97 ) = -0.121869
cos(98 ) = -0.139173
cos(99 ) = -0.156434
cos(100 ) = -0.173648
cos(101 ) = -0.190809
cos(102 ) = -0.207912
cos(103 ) = -0.224951
cos(104 ) = -0.241922
cos(105 ) = -0.258819
cos(106 ) = -0.275637
cos(107 ) = -0.292372
cos(108 ) = -0.309017
cos(109 ) = -0.325568
cos(110 ) = -0.34202
cos(111 ) = -0.358368
cos(112 ) = -0.374607
cos(113 ) = -0.390731
cos(114 ) = -0.406737
cos(115 ) = -0.422618
cos(116 ) = -0.438371
cos(117 ) = -0.45399
cos(118 ) = -0.469472
cos(119 ) = -0.48481
cos(120 ) = -0.5
cos(121 ) = -0.515038
cos(122 ) = -0.529919
cos(123 ) = -0.544639
cos(124 ) = -0.559193
cos(125 ) = -0.573576
cos(126 ) = -0.587785
cos(127 ) = -0.601815
cos(128 ) = -0.615661
cos(129 ) = -0.62932
cos(130 ) = -0.642788
cos(131 ) = -0.656059
cos(132 ) = -0.669131
(133 ) = -0.681998
cos(134 ) = -0.694658
cos(135 ) = -0.707107
cos(136 ) = -0.71934
cos(137 ) = -0.731354
cos(138 ) = -0.743145
cos(139 ) = -0.75471
cos(140 ) = -0.766044
cos(141 ) = -0.777146
cos(142 ) = -0.788011
cos(143 ) = -0.798636
cos(144 ) = -0.809017
cos(145 ) = -0.819152
cos(146 ) = -0.829038
cos(147 ) = -0.838671
cos(148 ) = -0.848048
cos(149 ) = -0.857167
cos(150 ) = -0.866025
cos(151 ) = -0.87462
cos(152 ) = -0.882948
cos(153 ) = -0.891007
cos(154 ) = -0.898794
cos(155 ) = -0.906308
cos(156 ) = -0.913545
cos(157 ) = -0.920505
cos(158 ) = -0.927184
cos(159 ) = -0.93358
cos(160 ) = -0.939693
cos(161 ) = -0.945519
cos(162 ) = -0.951057
cos(163 ) = -0.956305
cos(164 ) = -0.961262
cos(165 ) = -0.965926
cos(166 ) = -0.970296
cos(167 ) = -0.97437
cos(168 ) = -0.978148
cos(169 ) = -0.981627
cos(170 ) = -0.984808
cos(171 ) = -0.987688
cos(172 ) = -0.990268
cos(173 ) = -0.992546
cos(174 ) = -0.994522
cos(175 ) = -0.996195
cos(176 ) = -0.997564
cos(177 ) = -0.99863
cos(178 ) = -0.999391
cos(179 ) = -0.999848
cos(180 ) = -1
cos(181 ) = -0.999848
cos(182 ) = -0.999391
cos(183 ) = -0.99863
cos(184 ) = -0.997564
cos(185 ) = -0.996195
cos(186 ) = -0.994522
cos(187 ) = -0.992546
cos(188 ) = -0.990268
cos(189 ) = -0.987688
cos(190 ) = -0.984808
cos(191 ) = -0.981627
cos(192 ) = -0.978148
cos(193 ) = -0.97437
cos(194 ) = -0.970296
cos(195 ) = -0.965926
cos(196 ) = -0.961262
cos(197 ) = -0.956305
cos(198 ) = -0.951057
cos(199 ) = -0.945519
cos(200 ) = -0.939693
cos(201 ) = -0.93358
cos(202 ) = -0.927184
cos(203 ) = -0.920505
cos(204 ) = -0.913545
cos(205 ) = -0.906308
cos(206 ) = -0.898794
cos(207 ) = -0.891007
cos(208 ) = -0.882948
cos(209 ) = -0.87462
cos(210 ) = -0.866025
cos(211 ) = -0.857167
cos(212 ) = -0.848048
cos(213 ) = -0.838671
cos(214 ) = -0.829038
cos(215 ) = -0.819152
cos(216 ) = -0.809017
cos(217 ) = -0.798636
cos(218 ) = -0.788011
cos(219 ) = -0.777146
cos(220 ) = -0.766044
cos(221 ) = -0.75471
cos(222 ) = -0.743145
cos(223 ) = -0.731354
cos(224 ) = -0.71934
cos(225 ) = -0.707107
cos(226 ) = -0.694658
cos(227 ) = -0.681998
cos(228 ) = -0.669131
cos(229 ) = -0.656059
cos(230 ) = -0.642788
cos(231 ) = -0.62932
cos(232 ) = -0.615661
cos(233 ) = -0.601815
cos(234 ) = -0.587785
cos(235 ) = -0.573576
cos(236 ) = -0.559193
cos(237 ) = -0.544639
cos(238 ) = -0.529919
cos(239 ) = -0.515038
cos(240 ) = -0.5
cos(241 ) = -0.48481
cos(242 ) = -0.469472
cos(243 ) = -0.45399
cos(244 ) = -0.438371
cos(245 ) = -0.422618
cos(246 ) = -0.406737
cos(247 ) = -0.390731
cos(248 ) = -0.374607
cos(249 ) = -0.358368
cos(250 ) = -0.34202
cos(251 ) = -0.325568
cos(252 ) = -0.309017
cos(253 ) = -0.292372
cos(254 ) = -0.275637
cos(255 ) = -0.258819
cos(256 ) = -0.241922
cos(257 ) = -0.224951
cos(258 ) = -0.207912
cos(259 ) = -0.190809
cos(260 ) = -0.173648
cos(261 ) = -0.156434
cos(262 ) = -0.139173
cos(263 ) = -0.121869
cos(264 ) = -0.104528
cos(265 ) = -0.087156
cos(266 ) = -0.069756
cos(267 ) = -0.052336
cos(268 ) = -0.034899
cos(269 ) = -0.017452
cos(270 ) = -0
cos(271 ) = 0.017452
cos(272 ) = 0.034899
cos(273 ) = 0.052336
cos(274 ) = 0.069756
cos(275 ) = 0.087156
cos(276 ) = 0.104528
cos(277 ) = 0.121869
cos(278 ) = 0.139173
cos(279 ) = 0.156434
cos(280 ) = 0.173648
cos(281 ) = 0.190809
cos(282 ) = 0.207912
cos(283 ) = 0.224951
cos(284 ) = 0.241922
cos(285 ) = 0.258819
cos(286 ) = 0.275637
cos(287 ) = 0.292372
cos(288 ) = 0.309017
cos(289 ) = 0.325568
cos(290 ) = 0.34202
cos(291 ) = 0.358368
cos(292 ) = 0.374607
cos(293 ) = 0.390731
cos(294 ) = 0.406737
cos(295 ) = 0.422618
cos(296 ) = 0.438371
cos(297 ) = 0.45399
cos(298 ) = 0.469472
cos(299 ) = 0.48481
cos(300 ) = 0.5
cos(301 ) = 0.515038
cos(302 ) = 0.529919
cos(303 ) = 0.544639
cos(304 ) = 0.559193
cos(305 ) = 0.573576
cos(306 ) = 0.587785
cos(307 ) = 0.601815
cos(308 ) = 0.615661
cos(309 ) = 0.62932
cos(310 ) = 0.642788
cos(311 ) = 0.656059
cos(312 ) = 0.669131
cos(313 ) = 0.681998
cos(314 ) = 0.694658
cos(315 ) = 0.707107
cos(316 ) = 0.71934
cos(317 ) = 0.731354
cos(318 ) = 0.743145
cos(319 ) = 0.75471
cos(320 ) = 0.766044
cos(321 ) = 0.777146
cos(322 ) = 0.788011
cos(323 ) = 0.798636
cos(324 ) = 0.809017
cos(325 ) = 0.819152
cos(326 ) = 0.829038
cos(327 ) = 0.838671
cos(328 ) = 0.848048
cos(329 ) = 0.857167
cos(330 ) = 0.866025
cos(331 ) = 0.87462
cos(332 ) = 0.882948
cos(333 ) = 0.891007
cos(334 ) = 0.898794
cos(335 ) = 0.906308
cos(336 ) = 0.913545
cos(337 ) = 0.920505
cos(338 ) = 0.927184
cos(339 ) = 0.93358
cos(340 ) = 0.939693
cos(341 ) = 0.945519
cos(342 ) = 0.951057
cos(343 ) = 0.956305
cos(344 ) = 0.961262
cos(345 ) = 0.965926
cos(346 ) = 0.970296
cos(347 ) = 0.97437
cos(348 ) = 0.978148
cos(349 ) = 0.981627
cos(350 ) = 0.984808
cos(351 ) = 0.987688
cos(352 ) = 0.990268
cos(353 ) = 0.992546
cos(354 ) = 0.994522
cos(355 ) = 0.996195
cos(356 ) = 0.997564
cos(357 ) = 0.99863
cos(358 ) = 0.999391
cos(359 ) = 0.999848
cos(360 ) = 1