Question

Which of the following trigonometric functions will have range identical to the curve $y=2\cos x$

• A. $\cos 2x$
• B. $\sin 2x$
• C. $2\sin x$
• D. $2|\sin x|$

Answer 1

The correct option is C $2\sin x$

Range of $\cos x$ is $[-1,1]$
$\Rightarrow$ Range of $2\cos x$ is $[-2,2]$

Range of both $\cos 2x$ and $\sin 2x$ is $[-1,1]$

Range of $2\sin x$ is $[-2,2]$

Range of $2|\sin x|$ is $[0,2]$ $(\because |y|\ge 0)$