Question

find the following without using a calculator. \\( \sin ( \sin ^ { - 1 } 0.7 ) = ? \\)

Explanation:

Step1: Recall the property of inverse trigonometric functions

If \(y = \sin^{-1}x\), then \(\sin(y)=x\) for \(x\in[- 1,1]\) and \(y\in[-\frac{\pi}{2},\frac{\pi}{2}]\). Here \(x = 0.7\) which is in the domain \([-1,1]\) of \(\sin^{-1}x\).
Let \(y=\sin^{-1}(0.7)\), then by the definition of the inverse sine function, \(\sin(y)=0.7\).

Answer:

\(0.7\)