3 multiple choice 1 point what is sin⁻¹ - √2/2? -π/4 -π/3 π/4 π/3 none of these.
3 multiple choice 1 point what is sin⁻¹ - √2/2? -π/4 -π/3 π/4 π/3 none of these.
Answer
Explanation:
Step1: Recall inverse - sine function range
The range of (y = \sin^{-1}(x)) is (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).
Step2: Find the angle
We know that (\sin\left(-\frac{\pi}{4}\right)=-\frac{\sqrt{2}}{2}). Since (-\frac{\pi}{4}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]), (\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)=-\frac{\pi}{4}).
Answer:
A. (-\frac{\pi}{4})