evaluate without using a calculator. sin⁻¹(sin π/3)
evaluate without using a calculator. sin⁻¹(sin π/3)
Answer
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 (-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}).
Step2: Check the value of (\theta)
We have (\theta=\frac{\pi}{3}), and since (-\frac{\pi}{2}\approx - 1.57) and (\frac{\pi}{2}\approx1.57), and (-\frac{\pi}{2}<\frac{\pi}{3}<\frac{\pi}{2}).
Answer:
(\frac{\pi}{3})