Question

Fundamental period of the function $y=\left|\cot (\frac{x}{4}-\frac{\pi }{3})\right|$ is

• A. $\frac{\pi }{3}$
• B. $\frac{4\pi }{3}$
• C. $2\pi$
• D. $4\pi$

Answer 1

The correct option is D $4\pi$

If $f\left(x\right)$ has fundamental period $T,$ then $f(ax+b)$ has fundamental period $\frac{T}{|a|},$ where $a\ne 0$
We know that, the fundamental period of $|\cot x|$ is $\pi .$
Hence, the fundamental period of $\left|\cot (\frac{x}{4}-\frac{\pi }{3})\right|$ is $4\pi .$