Question

Determine weather the statement is true or false. Justify your answer

Answer 1

$\begin{gathered} \cos (-\frac{7\pi}{2})=\cos (\pi+\frac{\pi}{2}) \\ \cos (-\frac{7\pi}{2})=\cos (\frac{3\pi}{2}) \end{gathered}$

As we know:

$\begin{gathered} \cos (x)=0 \\ for \\ x=\pi n-\frac{\pi}{2} \\ n\in Z \end{gathered}$

For:

$\begin{gathered} n=2 \\ x=2\pi-\frac{\pi}{2}=\frac{3\pi}{2} \\ for \\ n=-3 \\ x=-3\pi-\frac{\pi}{2}=-\frac{7\pi}{2} \end{gathered}$

Therefore:

$\begin{gathered} \cos (-\frac{7\pi}{2})=0 \\ and \\ \cos (\frac{3\pi}{2})=0 \\ so\colon \\ 0=0 \\ This_{\text{ }}is_{\text{ }}true \end{gathered}$

Therefore, the statement is true