我发现采用博客学习也是种不错的方式。 同角 sin2α+cos2α=1\sin^2\alpha+\cos^2\alpha=1sin2α+cos2α=1 tanα=sinαcosα\tan\alpha=\frac{\sin\alpha}{\cos\alpha}tanα=cosαsinα 正弦 正弦定理。 asinA=bsinB=csinC=2R=D\frac a{\sin A}=\frac b{\sin B}=\frac c{\sin C}=2R=DsinAa=sinBb=sinCc=2R=D 余弦 余弦定理。 a2=b2+c2−2bccosA\begin{array}{l}a^2=b^2+c^2-2bc\cos A\end{array}a2=b2+c2−2bccosA b2=a2+c2−2accosB\begin{array}{l}b^2=a^2+c^2-2ac\cos B\end{array}b2=a2+c2−2accosB c2=a2+b2−2abcosC\begin{array}{l}c^2=a^2+b^2-2ab\cos C\end{array}c2=a2+b2−2abcosC 万能 sin2α=2tanα1+tan2α\sin2\alpha=\frac{2\tan\alpha}{1+\tan^2\alpha}sin2α=1+tan2α2tanα cos2α=1−tan2α1+tan2α\cos2\alpha=\frac{1-\tan^2\alpha}{1+\tan^2\alpha}cos2α=1+tan2α1−tan2α tan2α=2tanα1−tan2α\tan2\alpha=\frac{2\tan\alpha}{1-\tan^2\alpha}tan2α=1−tan2α2tanα 倍数 sin(α+β)=sinαcosβ+cosαsinβ;sin(α−β)=sinαcosβ−cosαsinβ\begin{array}{l}\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta;\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta\end{array}sin(α+β)=sinαcosβ+cosαsinβ;sin(α−β)=sinαcosβ−cosαsinβ cos(α+β)=cosαcosβ−sinαsinβ;cos(α−β)=cosαcosβ+sinαsinβ\begin{array}{l}\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta;\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta\end{array}cos(α+β)=cosαcosβ−sinαsinβ;cos(α−β)=cosαcosβ+sinαsinβ sin2α=2sinαcosα\begin{array}{l}\sin2\alpha=2\sin\alpha\cos\alpha\end{array}sin2α=2sinαcosα cos2α=cos2α−sin2α=2cos2α−1=1−2sin2α\begin{array}{l}\cos2\alpha=\cos^2\alpha-\sin^2\alpha=2\cos^2\alpha-1=1-2\sin^2\alpha\end{array}cos2α=cos2α−sin2α=2cos2α−1=1−2sin2α sinα2=±1−cosα2\begin{array}{l}\sin\frac\alpha2=\pm\sqrt{\frac{1-\cos\alpha}2}\end{array}sin2α=±21−cosα cosα2=±1+cosα2\begin{array}{l}\cos\frac\alpha2=\pm\sqrt{\frac{1+\cos\alpha}2}\end{array}cos2α=±21+cosα tanα2=1−cosαsinα=sinα1−cosα\begin{array}{l}\tan\frac\alpha2=\frac{1-\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\end{array}tan2α=sinα1−cosα=1−cosαsinα 辅助 asinθ+bcosθ=a2+b2sin(θ+φ)a\sin\theta+b\cos\theta=\sqrt{a^2+b^2}\sin(\theta+\varphi)asinθ+bcosθ=a2+b2sin(θ+φ)