Question

数学题，求各路大神解答 谢谢

这两道题的解答，最好有过程，中英皆可。谢谢大家。

Answer 1

1. a) sin^-1 x stands for the inverse of sin x, while (sinx)^-1 stands for the reciprocal of sinx.

   b) sin^-1 x = arcsinx, and  (sinx)^-1 = cscx

   c) sin^-1 (1/2) = pi/6, because the range of inverse sine is [-pi/2, pi/2]

2. a) Let x = tan^-1 (3/7). Then, tanx = 3/7, sinx = 3/√(3^2+7^2) 

   b) Let a = cos^-1(x^2-1) ==> cos a = (x^2-1), sin a = √[1-(x^2-1)^2]