Question

Find the period of : $f\left(x\right)=\cos \left(\frac{4x+9}{5}\right)$

Answer 1

If a function $f\left(x\right)$ is periodic with $T$ , then the function $f(ax+b)$ is periodic with $\frac{T}{\left|a\right|}$

$cos\left(x\right)$ is periodic with $2\pi$

So, $\cos \left(\frac{4x+9}{5}\right)=\cos (\frac{4x}{5}+\frac{9}{5})$ is periodic with

$\frac{2\pi }{\frac{4}{5}}$

$=\frac{5}{4}\times 2\pi$

$=\frac{5\pi }{2}$