Question

The period of $\cos h\left(\frac{\theta }{3}\right)$ is,

• A. $6\mathrm{\pi i}$
• B. $2\mathrm{\pi i}$
• C. $\mathrm{\pi i}$
• D. $9\mathrm{\pi i}$

Answer 1

The correct option is A

$6\mathrm{\pi i}$

Explanation for the correct option:

Given, $\cos h\left(\frac{\theta }{3}\right)$

As we know that the period of $\cos h\left(\theta \right)$ is $2\mathrm{\pi i}$.

i.e., $T\left(\cos h\left(\theta \right)\right)=2\mathrm{\pi i}$

$\Rightarrow$ $T\left(\cos h\left(\frac{1}{3}\times \theta \right)\right)=2\mathrm{\pi i}÷\frac{1}{3}$

$\Rightarrow$ $T\left(\cos h\left(\frac{\theta }{3}\right)\right)=2\mathrm{\pi i}\times \frac{3}{1}$

$\Rightarrow$ $T\left(\cos h\left(\frac{\theta }{3}\right)\right)=6\mathrm{\pi i}$

i.e., the period of $\cos h\left(\frac{\theta }{3}\right)$ is $6\mathrm{\pi i}$.

Hence, option (A) is the correct option.