Question

The domain in which sine function will be one-one, is

• A. $\left[\frac{-\pi }{2},\frac{\pi }{2}\right]$
• B. $\left[\frac{\pi }{2},\frac{3\pi }{2}\right]$
• C. $[0,\pi ]$
• D. Both 'a' and 'b'

Answer 1

Answer: (D)

Since, the domain of sine function is the set of all real numbers and range is the closed interval $[-1,1]$. If we restrict its domain to $\left[\frac{-\pi }{2},\frac{\pi }{2}\right]$, then it becomes one-one and onto with range $[-1,1]$. Actually, sine function restricted to any of the intervals $\left[\frac{-3\pi }{2},-\frac{\pi }{2}\right],\left[\frac{-\pi }{2},\frac{\pi }{2}\right],\left[\frac{\pi }{2},\frac{3\pi }{2}\right]$ etc., is one-one and its range is $[-1,1]$.