Question

find the following in degrees without using a calculator.
\\( \sin ^ { - 1 } ( \sin 17 ^ { \circ } ) = ? ^ { \circ } \\)

Explanation:

Step1: Recall the property of inverse sine function

The property of the inverse sine function \(y = \sin^{-1}(x)\) is that \(\sin^{-1}(\sin\theta)=\theta\) when \(- 90^{\circ}\leq\theta\leq90^{\circ}\).

Step2: Check the value of \(\theta\)

Here \(\theta = 17^{\circ}\), and \(-90^{\circ}<17^{\circ}<90^{\circ}\).

Answer:

\(17\)