if sin(π/8)=0.3827 what is the exact value of sin⁻¹(0.3827)?
if sin(π/8)=0.3827 what is the exact value of sin⁻¹(0.3827)?
Answer
Explanation:
Step1: Recall inverse - sine definition
The inverse - sine function (y = \sin^{-1}(x)) is defined such that if (y=\sin^{-1}(x)), then (\sin(y)=x) and (y\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]). Given that (\sin\left(\frac{\pi}{8}\right)=0.3827), by the definition of the inverse - sine function, (\sin^{-1}(0.3827)=\frac{\pi}{8}) since (\frac{\pi}{8}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).
Answer:
(\frac{\pi}{8})