余弦值角度对照表0到360度大全2023最新

在数学课上我们常提到的正弦，余弦0度，90度，180度分别等于多少。余弦值0到180、360的值是多呢，很多小伙伴想了解关于余弦值角度对照表的一些详细内容，下面是小编整理的与余弦值角度对照表相关的信息分享给大家，希望对大家有所帮助呢。

正弦，余弦0度，90度，180度分别等于多少

sin0°=0，cos0°=1;sin90°=1，cos90°=0;sin180°=0，cos180°=-1。

结果分析

1、当角度为0°时，角的两边重合，在y轴的取值为0，所以sin0°=0。

2、cosx=邻边/斜边，x=0时，斜边和邻边相等，所以cos0°=1。

3、sinα=r/y，r是单位圆的半径。当α=90度时，r=y，所以sin90度=1。

4、余弦是邻边与斜边之比，90°直角的对边是斜边，长度为0，所以cos90°=0。

5、sin180°=sin(90°+90°)=sin90°cos90°+cos90°sin90°=0，所以sin180°=0。

6、设180°角的终边上一点P(x，0)到原点的距离是r则r=-x，根据三角函数的定义得cos180°=x/r=x/(-x)=-1，所以，cos180°=-1。

公式关系

1、平方和关系

(sinα)^2+(cosα)^2=1

2、积的关系

sinα=tanα×cosα(即sinα/cosα=tanα)

cosα=cotα×sinα(即cosα/sinα=cotα)

tanα=sinα×secα(即tanα/sinα=secα)

正弦函数的定理及运用

在一个三角形中，各边和它所对角的正弦的比相等，即a/sinA=b/sinB=c/sinC

S△=c^2sinAsinB/2sin(A+B)(S△为三角形的面积，三个角为∠A∠B∠C，对边分别为a,b,c，)

S△=1/2acsinB=1/2bcsinA=1/2absinC(三个角为∠A∠B∠C，对边分别为a,b,c，参见三角函数)

另外，当sin值在180~360之间会出现负数，在360以上则会重复。

诱导公式

sin(2kπ+α)=sinα

cos(2kπ+α)=cosα

tan(2kπ+α)=tanα

cot(2kπ+α)=cotα

sec(2kπ+α)=secα

正弦余弦的所有特殊角的值

特殊角的值如下：

在直角三角形中，任意一锐角∠A的对边与斜边的比叫做∠A的正弦，记作sinA(由英语sine一词简写得来)，即sinA=∠A的对边/斜边。

扩展资料

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)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγ

cos(α±β)=cosαcosβsinβsinα

tan(α±β)=(tanα±tanβ)/(1tanαtanβ)

余弦值角度对照表

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