Given is the partial graph of an even periodic function $f$ whose period is $8$. If $\left[*\right]$ denotes greatest integer function then find the value of the expression $f\left(-3\right)+2\left|f\left(-1\right)\right|+\left[f\left(\frac{7}{8}\right)\right]+f\left(0\right)+\arccos \left(f\left(-2\right)\right)+f\left(-7\right)+f\left(20\right).$

 

Let $f\left(x\right)=\sin x+\cos ax$ be a periodic function. Then,

The function $f\left(x\right)=\left|sin4x\right|+\left|cos2x\right|,$ is a periodic function with a fundamental period 

If f be a real value function such that for any real $x,f(15 + x) = f(15 - x) \& f(30 + x)= -f(30 - x)$, then which of the following statement is true ?