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

Question

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

Explanation:

Step1: Recall the property of inverse trigonometric functions

For \(y = \sin^{-1}x\), where \(x\in[- 1,1]\) and \(y\in[-\frac{\pi}{2},\frac{\pi}{2}]\), the property \(\sin(\sin^{-1}x)=x\) holds.

Step2: Apply the property to the given expression

Here \(x = 0.7\) (since \(0.7\in[-1,1]\)), so \(\sin(\sin^{-1}0.7)=0.7\).

Answer:

\(0.7\)