evaluate. sin^(-1)(sin(3π/4)) sin^(-1)(sin(3π/4)) = □ (simplify your answer. type your answer in radians…

evaluate. sin^(-1)(sin(3π/4)) sin^(-1)(sin(3π/4)) = □ (simplify your answer. type your answer in radians. type an exact answer, using π fractions for any numbers in the expression.)

evaluate. sin^(-1)(sin(3π/4)) sin^(-1)(sin(3π/4)) = □ (simplify your answer. type your answer in radians. type an exact answer, using π fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall the domain of inverse - sine function

The domain of (y = \sin^{-1}(x)) is ([- 1,1]) and its range is (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]). We know that (\sin\left(\frac{3\pi}{4}\right)=\sin\left(\pi - \frac{\pi}{4}\right)=\sin\left(\frac{\pi}{4}\right)).

Step2: Evaluate the inverse - sine

Since (\sin\left(\frac{3\pi}{4}\right)=\sin\left(\frac{\pi}{4}\right)) and (\frac{\pi}{4}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]), then (\sin^{-1}\left(\sin\left(\frac{3\pi}{4}\right)\right)=\frac{\pi}{4}).

Answer:

(\frac{\pi}{4})