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第4章:坐标变换
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 \thetain terms of a.
已知 -\frac{3\pi}{2}<\theta<-\pisin\theta = a, 试用 a 表示 \theta.
Answer :
-sin^{-1}a-\pi
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