学习和计算时特别常用的三角公式( 二 ) _三角公式

sin ? ( π ? α ) = sin ? α cos ? ( π ? α ) = ? cos ? α tan ? ( π ? α ) = ? tan ? α cot ? ( π ? α ) = ? cot ? α sec ? ( π ? α ) = ? sec ? α csc ? ( π ? α ) = csc ? α ￣ \{\begin{} \sin \left( \pi -\alpha \right) &=\sin \alpha\\ \cos \left( \pi -\alpha \right) &=-\cos \alpha\\ \tan \left( \pi -\alpha \right) &=-\tan \alpha\\ \cot \left( \pi -\alpha \right) &=-\cot \alpha\\ \sec \left( \pi -\alpha \right) &=-\sec \alpha\\ \csc \left( \pi -\alpha \right) &=\csc \alpha\\ \end{}} sin(π?α)cos(π?α)tan(π?α)cot(π?α)sec(π?α)csc(π?α)?=sinα=?cosα=?tanα=?cotα=?secα=cscα??
sin ? ( 2 π ? α ) = ? sin ? α cos ? ( 2 π ? α ) = cos ? α tan ? ( 2 π ? α ) = ? tan ? α cot ? ( 2 π ? α ) = ? cot ? α sec ? ( 2 π ? α ) = sec ? α csc ? ( 2 π ? α ) = ? csc ? α ￣ \{\begin{} \sin \left( 2\pi -\alpha \right) &=-\sin \alpha\\ \cos \left( 2\pi -\alpha \right) &=\cos \alpha\\ \tan \left( 2\pi -\alpha \right) &=-\tan \alpha\\ \cot \left( 2\pi -\alpha \right) &=-\cot \alpha\\ \sec \left( 2\pi -\alpha \right) &=\sec \alpha\\ \csc \left( 2\pi -\alpha \right) &=-\csc \alpha\\ \end{}} sin(2π?α)cos(2π?α)tan(2π?α)cot(2π?α)sec(2π?α)csc(2π?α)?=?sinα=cosα=?tanα=?cotα=secα=?cscα??
sin ? ( π 2 + α ) = cos ? α cos ? ( π 2 + α ) = ? sin ? α tan ? ( π 2 + α ) = ? cot ? α cot ? ( π 2 + α ) = ? tan ? α sec ? ( π 2 + α ) = ? csc ? α csc ? ( π 2 + α ) = sec ? α ￣ \{\begin{} \sin \left( \frac{\pi}{2}+\alpha \right) &=\cos \alpha\\ \cos \left( \frac{\pi}{2}+\alpha \right) &=-\sin \alpha\\ \tan \left( \frac{\pi}{2}+\alpha \right) &=-\cot \alpha\\ \cot \left( \frac{\pi}{2}+\alpha \right) &=-\tan \alpha\\ \sec \left( \frac{\pi}{2}+\alpha \right) &=-\csc \alpha\\ \csc \left( \frac{\pi}{2}+\alpha \right) &=\sec \alpha\\ \end{}} sin(2π?+α)cos(2π?+α)tan(2π?+α)cot(2π?+α)sec(2π?+α)csc(2π?+α)?=cosα=?sinα=?cotα=?tanα=?cscα=secα??
sin ? ( π 2 ? α ) = cos ? α cos ? ( π 2 ? α ) = sin ? α tan ? ( π 2 ? α ) = cot ? α cot ? ( π 2 ? α ) = tan ? α csc ? ( π 2 ? α ) = sec ? α sec ? ( π 2 ? α ) = csc ? α ￣ \{\begin{} \sin \left( \frac{\pi}{2}-\alpha \right) &=\cos \alpha\\ \cos \left( \frac{\pi}{2}-\alpha \right) &=\sin \alpha\\ \tan \left( \frac{\pi}{2}-\alpha \right) &=\cot \alpha\\ \cot \left( \frac{\pi}{2}-\alpha \right) &=\tan \alpha\\ \csc \left( \frac{\pi}{2}-\alpha \right) &=\sec \alpha\\ \sec \left( \frac{\pi}{2}-\alpha \right) &=\csc \alpha\\ \end{}} sin(2π??α)cos(2π??α)tan(2π??α)cot(2π??α)csc(2π??α)sec(2π??α)?=cosα=sinα=cotα=tanα=secα=cscα??
两角和公式(加法公式)[三组]
sin ? ( α + β ) = sin ? α cos ? β + cos ? α sin ? β \sin \left( \alpha +\beta \right) =\sin \alpha \cos \beta +\cos \alpha \sin \beta sin(α+β)=sinαcosβ+cosαsinβ
sin ? ( α ? β ) = sin ? α cos ? β ? cos ? α sin ? β \sin \left( \alpha -\beta \right) =\sin \alpha \cos \beta -\cos \alpha \sin \beta sin(α?β)=sinαcosβ?cosαsinβ
cos ? ( α + β ) = cos ? α cos ? β ? sin ? α sin ? β \cos \left( \alpha +\beta \right) =\cos \alpha \cos \beta -\sin \alpha \sin \beta cos(α+β)=cosαcosβ?sinαsinβ
cos ? ( α ? β ) = cos ? α cos ? β + sin ? α sin ? β \cos \left( \alpha -\beta \right) =\cos \alpha \cos \beta +\sin \alpha \sin \beta cos(α?β)=cosαcosβ+sinαsinβ
tan ? ( α + β ) = tan ? α + tan ? β 1 ? tan ? α tan ? β \tan \left( \alpha +\beta \right) =\frac{\tan \alpha +\tan \beta}{1-\tan \alpha \tan \beta} tan(α+β)=1?tanαtanβtanα+tanβ?
tan ? ( α ? β ) = tan ? α ? tan ? β 1 + tan ? α tan ? β \tan \left( \alpha -\beta \right) =\frac{\tan \alpha -\tan \beta}{1+\tan \alpha \tan \beta} tan(α?β)=1+tanαtanβtanα?tanβ?
倍角公式
sin ? 2 α = 2 sin ? α cos ? α \sin 2\alpha =2\sin \alpha \cos \alpha sin2α=2sinαcosα
cos ? 2 α = cos ? 2 α ? sin ? 2 α \cos 2\alpha =\cos ^2\alpha -\sin ^2\alpha cos2α=cos2α?sin2α
= 2 cos ? 2 α ? 1 =2\cos ^2\alpha -1 =2cos2α?1