Chapter 13.2, Problem 14OE

To determine

To find: The following statements.

Answer to Problem 14OE

The $\left(s\right)$ , $\left(-\cos s,-\sin s\right)$ , $\cos \left(s+\pi \right)$ , $\sin \left(s+\pi \right)$ are the statements.

Explanation of Solution

Given information:

The given statement is

  $\begin{array}{l}\cos \left(s+\pi \right)=-\cos s\\ \sin \left(s+\pi \right)=-\sin s\end{array}$

  

Calculation:

From the given figure

The length of the unit circle shown at the right is $\left(s\right)$ .

Therefore in terms of $\left(s\right)$ , the coordinates of $Q$ are $\left(-\cos s,-\sin s\right)$ .

Therefore, in terms of

  $\begin{array}{c}\cos \left(s+\pi \right)=-x\\ =-\cos s\end{array}$ .

And

  $\begin{array}{c}\sin \left(s+\pi \right)=-y\\ =-\sin s\end{array}$ .

Therefore, the $\left(s\right)$ , $\left(-\cos s,-\sin s\right)$ , $\cos \left(s+\pi \right)$ , $\sin \left(s+\pi \right)$ are the statements.