外餘割

外余割为三角函数的一种，现很少使用。其符号通常表示为 $\operatorname {excosec} x$ , $\operatorname {exc} x$ 。与余割的关系： $\operatorname {excosec} x=\csc ^{-1}x$ 。

在单位圆上表示的三角函数。

\operatorname {excsc} (\theta )=\operatorname {exsec} \left({\frac {\pi }{2}}-\theta \right)=\csc(\theta )-1={\frac {1}{\sin(\theta )}}-1.

导数

{\frac {\mathrm {d} }{\mathrm {d} \theta }}\operatorname {excsc} (\theta )=-\cot(\theta )\csc(\theta )={\frac {-\cos(\theta )}{\sin ^{2}(\theta )}}

与其他三角函数的关系

\operatorname {excsc} (\theta )={\frac {1-\sin(\theta )}{\sin(\theta )}}={\frac {\operatorname {coversin} (\theta )}{\sin(\theta )}}=\operatorname {coversin} (\theta )\csc(\theta )=2\left(\cos \left({\frac {\theta }{2}}\right)\right)^{2}\csc(\theta ).\

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參考文獻

埃里克·韦斯坦因. . MathWorld.

另见

外正割

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