2.2 Calculation of Inverse Trigonometric Functions - 独中课程 | 线上补习

高三数学 | 高级数学

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2.2 Calculation of Inverse Trigonometric Functions

Find the value of the following statement
求下列各式的值

(1) $cos{[}{sin}^{-1}{(}-\frac{4}{5})-{cos}^{-1}{(}-\frac{3}{5})]$

Answer :

-1

(2) $sin{(}{sin}^{-1}{\frac{4}{5}}+{cos}^{-1}{\frac{5}{13}})$

Answer :

$\frac{56}{65}$

(3) $cos{(}2{sin}^{-1}{\frac{1}{3}}-{tan}^{-1}{\frac{15}{8}})$

Answer :

$\frac{56+60\sqrt2}{153}$

(4) $tan{[}2{tan}^{-1}{\frac{1}{5}}-{cos}^{-1}{(}-\frac{8}{17})]$

Answer :

$10\frac{10}{21}$

(5) $sin{(}{tan}^{-1}{(}-\frac{12}{5})-{sin}^{-1}{(}-\frac{2}{3}))$

Answer :

$\frac{10-12\sqrt5}{39}$

(6) ${tan}^{-1}{(}\sqrt2-1)-{tan}^{-1}{(}\frac{\sqrt2}{2-\sqrt2})$

Answer :

$-\frac{\pi}{4}$

(7) Given that $-\frac{3\pi}{2}<\theta<-\pi$ and $sin\theta = a$ , find $\theta$ in terms of a.
已知 $-\frac{3\pi}{2}<\theta<-\pi$ 和 $sin\theta = a$ , 试用 a 表示 $\theta$ .

Answer :

$-sin^{-1}a-\pi$