标签：phi cot -- spl alpha arp sqrt 符号 数值
设角 \(\alpha\) 的终边与单位圆交于点 \(P(x,y)\) ，则有
\[\sin{\alpha}=y,\cos{\alpha}=x\]
\[\tan{\alpha}=\frac{y}{x},\cot{\alpha}=\frac{x}{y}\]
\[\sec{\alpha}=\frac{1}{x},\csc{\alpha}=\frac{1}{y}\]
倒数关系
\[\tan{\alpha} \cot{\alpha}=1\]
\[\sin{\alpha} \csc{\alpha}=1\]
\[\cos{\alpha} \sec{\alpha}=1\]
商的关系
\[\frac{\sin{\alpha}}{\cos{\alpha}}=\tan{\alpha}=\frac{\sec{\alpha}}{\csc{\alpha}}=\frac{1}{\cot{\alpha}}\]
平方关系
\[\sin^2{\alpha}+\cos^2{\alpha}=1\]
记忆口诀：奇变偶不变，符号看象限。
\(\alpha\) 与 \(\alpha + \pi\) 间三角函数值的关系
\[\sin{(\alpha + \pi)}=-\sin{\alpha}\]
\[\cos{(\alpha + \pi)}=-\cos{\alpha}\]
\[\tan{(\alpha+\pi)}=\tan{\alpha}\]
\[\cot{(\alpha+\pi)}=\cot{\alpha}\]
\(\alpha\) 与 \(-\alpha\) 间三角函数值的关系
\[\sin{(-\alpha)}=-\sin{\alpha}\]
\[\cos{(-\alpha)}=\cos{\alpha}\]
\[\tan{(-\alpha)}=-\tan{\alpha}\]
\[\cot{(-\alpha)}=-\cot{\alpha}\]
\(\alpha\) 与 \(\pi-\alpha\) 间三角函数的关系
\[\sin{(\pi-\alpha)}=\sin{\alpha}\]
\[\cos(\pi-\alpha)=-\cos{\alpha}\]
\[\tan(\pi-\alpha)=-\tan{\alpha}\]
\[\cot{(\pi-\alpha)}=-\cot{\alpha}\]
\(\alpha\) 与 \(\frac{\pi}{2}\pm\alpha\) 间三角函数的关系
\[\sin{(\alpha+\frac{\pi}{2})}=\cos{\alpha}\]
\[\cos{(\alpha+\frac{\pi}{2})}=-\sin{\alpha}\]
\[\tan{(\alpha+\frac{\pi}{2})}=-\cot{\alpha}\]
\[\cot{(\alpha+\frac{\pi}{2})}=-\tan{\alpha}\]
\[\sin{(\frac{\pi}{2}-\alpha)}=\cos{\alpha}\]
\[\cos{(\frac{\pi}{2}-\alpha)}=\sin{\alpha}\]
\[\tan{(\frac{\pi}{2}-\alpha)}=\cot{\alpha}\]
\[\cot{(\frac{\pi}{2}-\alpha)}=\tan{\alpha}\]
\[\cos{(x\pm y)}=\cos{x}\cos{y} \ \mp \ \sin{x}\sin{y}\]
\[\sin(x\pm y)=\sin{x}\sin{y} \ \pm \ \cos{x}\cos{y}\]
\[\tan{(x\pm y)}=\frac{\tan{x} \ \pm \ \tan{y}}{1 \ \mp \ \tan{x}\tan{y}}\]
\[\sin{2x}=2\sin{x}\cos{x}\]
\[\cos{2x}=\cos^2{x}-\sin^2{x}=2cos^2{x}-1=1-2\sin^2{x}\]
\[\tan{2x}=\frac{2\tan{x}}{1-\tan^2{x}}\]
\[\sin^2{\frac{x}{2}}=\frac{1-\cos{x}}{2}\]
\[\cos^2{\frac{x}{2}}=\frac{1+\cos{x}}{2}\]
\[\tan^2{\frac{x}{2}}=\frac{1-\cos{x}}{1+\cos{x}}\]
\[1+\cos{2x}=2\cos^2{x}\]
\[1-\cos{2x}=2\sin^2{x}\]
\[a\sin{x}+b\cos{x}=\sqrt{a^2+b^2}\sin{(x+\varphi)}\]
其中， \(\cos{\varphi}=\frac{a}{\sqrt{a^2+b^2}}\) ， \(\sin{\varphi}=\frac{b}{\sqrt{a^2+b^2}}\) 。
\[\cos{x}=\frac{1-\tan^2{\frac{x}{2}}}{1+\tan^2{\frac{x}{2}}}\]
\[\sin{x}=\frac{2\tan{\frac{x}{2}}}{1+\tan^2{\frac{x}{2}}}\]
\[\tan{x}=\frac{\sin{x}}{\cos{x}}=\frac{2\tan{\frac{x}{2}}}{1-\tan^2{\frac{x}{2}}}\]
标签：phi cot -- spl alpha arp sqrt 符号 数值
原文地址：https://www.cnblogs.com/hlw1/p/12259584.html
