Question

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

Answer 1

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

As we know:

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

For:

`\begin{gathered} n=2 \\ x=2\pi-(\pi)/(2)=(3\pi)/(2) \\ for \\ n=-3 \\ x=-3\pi-(\pi)/(2)=-(7\pi)/(2) \end{gathered}`

Therefore:

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

Therefore, the statement is true