Question

The period of the function $f\left(x\right)=4\cos (2x+3)$ is

• A. $2\pi$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. none of these

Answer 1

Answer: (C)

$\pi$

$f\left(x\right)=f(T+x)$

$\Rightarrow 4\cos (2x+3)=4\cos (2T+2x+3)$

$\Rightarrow \cos (2x+3)=\cos (2T+2x+3)$

$\Rightarrow \cos (2\pi +2x+3)=\cos (2T+2x+3)$

$\Rightarrow 2\pi =2T$

$\therefore T=\pi$

Hence the period of $f\left(x\right)$ is $T=\pi$