Question

The period of the function
$f\left(x\right)=4{\sin }^4\left(\frac{4x-3\pi }{6{\pi }^2}\right)+2\cos \left(\frac{4x-3\pi }{3{\pi }^2}\right)$ is

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

Answer 1

The correct option is B $\frac{3{\pi }^3}{4}$

$f\left(x\right)=(2{\sin }^2(\frac{4x-3\pi }{6{\pi }^2}){)}^2+2\cos (\frac{4x-3\pi }{3{\pi }^2})=1+{\cos }^2(\frac{4x-3\pi }{3{\pi }^2})$

Period of $f\left(x\right)$ is $\frac{\pi }{\frac{4}{3{\pi }^2}}=\frac{3{\pi }^3}{4}$