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مقادیر سینوس و کسینوس برای زوایای خاص روی دایرهٔ واحد.
قضیه فیثاغورث[ویرایش]
![{\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9333418071b0b0662ba53f8983fe1cbb613ad005)
![{\displaystyle 1+\tan ^{2}\theta =\sec ^{2}\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0e65a44a4f54eea9ec39f392cb406af0be301e0)
![{\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/569181e0b7d46ae94b93ef730ec2f4374dca2ced)
تبدیل زاویه[ویرایش]
جمع و تفاضل دو زاویه[ویرایش]
![{\displaystyle \cos(\theta +\beta )=\cos \theta .\cos \beta -\sin \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73815b05a97c6c08b1fe4adefe492b356d09c254)
![{\displaystyle \cos(\theta -\beta )=\cos \theta .\cos \beta +\sin \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/721f66568f55ddbadeb07c1a331a92abbe26eb82)
![{\displaystyle \sin(\theta +\beta )=\sin \theta .\cos \beta +\cos \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61d3f85ddb9898794ae527714c7502b7023b0965)
![{\displaystyle \sin(\theta -\beta )=\sin \theta .\cos \beta -\cos \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f415226aa28dff571ce7f028423f486105c43064)
![{\displaystyle \tan(\theta +\beta )={\frac {\tan \theta +\tan \beta }{1-\tan \theta .\tan \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0dd3bd706b3facee6720a8625c772b8df2f4a442)
![{\displaystyle \tan(\theta -\beta )={\frac {\tan \theta -\tan \beta }{1+\tan \theta .\tan \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0f729bed70209d97446e169ae665713ca096fbe)
![{\displaystyle \cot(\theta +\beta )={\frac {\cot \theta .\cot \beta -1}{\cot \theta +\cot \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fbe8b6fc5145acdfbfc66eba0766a99396406c8)
![{\displaystyle \cot(\theta -\beta )={\frac {\cot \theta .\cot \beta +1}{\cot \beta -\cot \theta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9cf563182c0a22aa9fa3358d7597b27c0a55e3df)
زاویه دو برابر[ویرایش]
![{\displaystyle \sin(2\theta )=2\sin \theta \cos \theta ={\frac {2\tan \theta }{1+\tan ^{2}\theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91e580dd72f58b60417e06a5ba6c8e76109d650e)
![{\displaystyle \cos(2\theta )=\cos ^{2}\theta -\sin ^{2}\theta =2\cos ^{2}\theta -1=1-2\sin ^{2}\theta ={\frac {1-\tan ^{2}\theta }{1+\tan ^{2}\theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6f9e9ba9762d2e92822ebdc3edb3640478bdab4)
![{\displaystyle \tan(2\theta )={\frac {2\tan \theta }{1-\tan ^{2}\theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf0463617c8fb39ff3d7aa1f54294e865be07dbc)
![{\displaystyle \cot(2\theta )={\frac {\cot ^{2}\theta -1}{2\cot \theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ff367e8c14d2b88ca2ce13446f0bfeb4f5bcca3)
![{\displaystyle \sec(2\theta )={\frac {\sec ^{2}\theta }{2-\sec ^{2}\theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24c5bfee3c72392135f9acb3389a2269d5a04737)
![{\displaystyle \csc(2\theta )={\frac {\sec \theta \csc \theta }{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e70cd86224a650a834db5c53917909be89c74673)
زاویه سه برابر[ویرایش]
![{\displaystyle \sin 3\theta =3\sin \theta -4\sin ^{3}\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0906a888ebe34f011d3b621f8ec3184cdc4f6ac)
![{\displaystyle \cos 3\theta =4\cos ^{3}\theta -3\cos \theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/5c030df0e0640a7d3153d386ba3610b57650b256)
![{\displaystyle \tan 3\theta ={\frac {3\tan \theta -\tan ^{3}\theta }{1-3\tan ^{2}\theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/da5608e031f3cafc680c80f37dce9899f869de81)
![{\displaystyle \cos ^{2}\phi ={\frac {1}{2}}\ (1+\cos 2\phi )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d470ec2f61cf21265cedd8b2a9d0b47ada1b32a9)
![{\displaystyle \sin ^{2}\phi ={\frac {1}{2}}\ (1-\cos 2\phi )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f6689931fb94e2cdfc4b5c9d3a17c3f431fe2559)
![{\displaystyle \tan {\frac {\phi }{2}}\ ={\frac {\sin \phi }{1+\cos \phi }}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/899aa2255db33f72f36840289f1fe2c43e83068e)
تبدیل ضرب به جمع[ویرایش]
![{\displaystyle \sin a.\cos b={\frac {\sin(a+b)+\sin(a-b)}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b114ca396eecd29ee20e5e1763690fcbb7d9d090)
![{\displaystyle \cos a.\cos b={\frac {\cos(a+b)+\cos(a-b)}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3fb29edbc031dc3d25bd05b421ff1f5081769b13)
![{\displaystyle \sin a.\sin b={\frac {\cos(a-b)-\cos(a+b)}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d99eefca3e67828fd4a7e833949efd4fce0b5541)
تبدیل جمع به ضرب[ویرایش]
![{\displaystyle \sin a\pm \sin b=2\sin({\frac {a\pm b}{2}}).\cos({\frac {a\mp b}{2}}\,)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/434c38a7488ec5b4399f275977764e3e80643304)
![{\displaystyle \cos a+\cos b=2\cos({\frac {a+b}{2}}).\cos({\frac {a-b}{2}}\,)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8451dfc0da8d5739169cf052f0d12ca8ad0662a8)
![{\displaystyle \cos a-\cos b=-2\sin({\frac {a+b}{2}}).\sin({\frac {a-b}{2}}\,)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9cd04cf076d4189564d8b9f319227f71396ec663)
![{\displaystyle \tan a\pm \ tanb={\frac {\sin(a\pm b)}{\cos a\cos b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bda83cbce511b6a82488a4de9984b4ea3e5b6ea2)
جمع سینوس و کسینوس یک زاویه مهندسی[ویرایش]
![{\displaystyle \displaystyle \sin \theta \pm \cos \theta ={\sqrt {2}}sin(\theta \pm {\frac {\pi }{4}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c077087f778c299d812890c3f8e32e1ffdeee72d)
![{\displaystyle {\frac {1\pm \tan x}{1\mp \tan x}}=\tan(\pi /4\pm x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d29241697467fb4dc28c3ad4c204774145955f2d)
![{\displaystyle \tan(\pi /2-x)=\cot(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6be38263ca8ec67714694aa342ea46203dcee43c)
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