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 $\mathrm{sine}$ function by ${\sin }^{-1}$ (arc sine function).