Question

Consider the following statements
Statement I The inverse of sine function is define in the interval $[-\pi, 0],[0, \pi]$ etc.
Statement II The inverse of sine function is denoted by $\sin ^{-1}$.
Choose the correct option.

• A. Only I is true
• B. Only II is true
• C. Both I and II are true
• D. Neither I nor II is true

Answer 1

Answer: (B)

Sine function is one-one and onto in the interval $\left[\frac{-3 \pi}{2}, \frac{-\pi}{2}\right],\left[\frac{-\pi}{2}, \frac{\pi}{2}\right],\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]$ etc; and its range is $[-1,1]$. So, inverse of sine function is define in each of these intervals. We denote the inverse of $\operatorname{sine}$ function by $\sin ^{-1}$ (arc sine function).