三角函数常用公式
2021-05-27 17:52:07 110 举报AI智能生成
三角函数常用公式汇总（持续更新···）
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锐角三角函数：对边a，邻边b，斜边c
正弦：sinA=<span class="equation-text" contenteditable="false" data-equation="{A \over C}" data-index="0"><span></span><span></span></span>
余弦：cosA=<span class="equation-text" contenteditable="false" data-index="0" data-equation="{b \over c}"><span></span><span></span></span>
正切：tanA=<span class="equation-text" contenteditable="false" data-index="0" data-equation="{a \over b}"><span></span><span></span></span>
余切：cotA=<span class="equation-text" contenteditable="false" data-index="0" data-equation="{b\over a}"><span></span><span></span></span>
正割：secA=<span class="equation-text" contenteditable="false" data-index="0" data-equation="{c \over b}"><span></span><span></span></span>
余割：cscA=<span class="equation-text" contenteditable="false" data-equation="{c \over a}" data-index="0"><span></span><span></span></span>
同角关系
倒数关系
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan\alpha\cot\alpha=1"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin\alpha \csc\alpha=1"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cos\alpha \sec\alpha=1"><span></span><span></span></span>
商数关系
<span class="equation-text" contenteditable="false" data-equation="\tan\alpha={\sin\alpha \over \cos\alpha}" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot\alpha={\cos\alpha \over \sin\alpha}"><span></span><span></span></span>
平方关系
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin^{2}\alpha+\cos^{2}\alpha=1"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="1+\tan^{2}\alpha=\sec^{2}\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="1+\cot^{2}\alpha=\csc^{2}\alpha"><span></span><span></span></span>
诱导公式
sin族
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin(-\alpha)=-\sin\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin(\frac{\pi}{2}-\alpha)=\cos\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin(\frac{\pi}{2}+\alpha)=\cos\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin({\pi}-\alpha)=\sin\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin(\pi+\alpha)=-\sin\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin(\frac{3\pi}{2}-\alpha)=-\cos\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin(\frac{3\pi}{2}+\alpha)=-\cos\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin({2\pi}-\alpha)=-\sin\alpha"><span></span><span></span></span>
cos族
<span class="equation-text" contenteditable="false" data-equation="\cos(-\alpha)=\cos\alpha" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cos(\frac{\pi}{2}-\alpha)=\sin\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-equation="\cos(\frac{\pi}{2}+\alpha)=-\sin\alpha" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-equation="\cos({\pi}-\alpha)=-\cos\alpha" data-index="0"><span></span></span>
<span class="equation-text" contenteditable="false" data-equation="\cos({\pi}+\alpha)=-\cos\alpha" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-equation="\cos(\frac{3\pi}{2}-\alpha)=-\sin\alpha" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cos(\frac{3\pi}{2}+\alpha)=\sin\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cos({2\pi}-\alpha)=\cos\alpha"><span></span><span></span></span>
tan族
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan(-\alpha)=-\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan(\frac{\pi}{2}-\alpha)=\cot\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan(\frac{\pi}{2}+\alpha)=-\cot\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan({\pi}-\alpha)=-\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan({\pi}+\alpha)=\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan(\frac{3\pi}{2}-\alpha)=\cot\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan(\frac{3\pi}{2}+\alpha)=-\cot\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan({2\pi}-\alpha)=-\tan\alpha"><span></span><span></span></span>
cot族
<span class="equation-text" contenteditable="false" data-equation="\cot(-\alpha)=-\cot\alpha" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot(\frac{\pi}{2}-\alpha)=\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot(\frac{\pi}{2}+\alpha)=-\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot({\pi}-\alpha)=-\cot\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot({\pi}+\alpha)=\cot\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot(\frac{3\pi}{2}-\alpha)=\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot(\frac{3\pi}{2}+\alpha)=-\tan\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cot({2\pi}-\alpha)=-\cot\alpha"><span></span><span></span></span>
半角公式
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\sin\frac{\alpha}{2}=\pm{\sqrt{{1-\cos\alpha}\over 2}}"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-equation="\cos\frac{\alpha}{2}=\pm{\sqrt{{1+\cos\alpha}\over 2}}" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\tan\frac{\alpha}{2}=\pm{\sqrt{{1-\cos\alpha}\over {1+\cos\alpha}}}={1-\cos\alpha\over \sin\alpha}={\sin\alpha\over {1+\cos\alpha}}"><span></span><span></span></span>
降幂公式
<span class="equation-text" contenteditable="false" data-equation="\sin\alpha^2={1-\cos2\alpha\over 2}" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cos\alpha^2={1+\cos2\alpha\over 2}"><span></span><span></span></span>
倍角公式
<span class="equation-text" contenteditable="false" data-equation="\sin2\alpha=2\sin\alpha\cos\alpha" data-index="0"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\cos2\alpha=\cos^2\alpha-\sin^2\alpha=2\cos^2\alpha-1=1-2\sin^2\alpha"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-equation="\tan2\alpha={2\tan\alpha\over\ 1-\tan^2\alpha}" data-index="0"><span></span><span></span></span>
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