Chapter 13.2, Problem 17WE

To determine

To Find: The exact values of the six trignometric functions of $s$.

Answer to Problem 17WE

The six trignometric functions of $s$ is ;

  $\sin s=-\frac{4}{5}$$\cos s=\frac{3}{5}$$\tan s=\frac{-4}{3}$$\cot s=-\frac{3}{4}$$\sec s=\frac{5}{3}$$\cos ecs=-\frac{5}{4}$

Explanation of Solution

Given information:

The given is $P\left(\frac{3}{5},-\frac{4}{5}\right)$ .

Calculation:

We have sin $s=y$ , and cos $s=x$ . Substitute the values of $x$ and $y$ in the formula,

  $\sin s=-\frac{4}{5}$$\cos s=\frac{3}{5}$

we know that tan $s=\frac{\sin s}{\cos s}$ if $\cos s\ne 0.$ substitute $-\frac{4}{5}$ for $\sin s;$ and $\frac{3}{5}$ for $\cos s$ in the formula, and simplify.

  $\begin{array}{c}\tan s=\frac{-\frac{4}{5}}{\frac{3}{5}}\\ =\frac{-4}{3}\end{array}$

We know that $\cot s=\frac{\cos s}{\sin s}$ if $\sin s\ne 0$ . Substitute $-\frac{4}{5}$ for $\sin s,$ and $\frac{3}{5}$ for $\cos s$ in the formula, and simplify.

  $\begin{array}{c}\cot s=\frac{\frac{3}{5}}{\frac{-4}{5}}\\ =-\frac{3}{4}\end{array}$

Similarly, find other trignometric functions.

  $\begin{array}{c}\sec s=\frac{1}{\cos s}\\ =\frac{1}{\frac{3}{5}}\\ =\frac{5}{3}\end{array}$$\begin{array}{c}\cos ecs=\frac{1}{\sin s}\\ =\frac{1}{\frac{-4}{5}}\\ =-\frac{5}{4}\end{array}$

Therefore, the six trignometric functions of $s$ is ;

  $\sin s=-\frac{4}{5}$$\cos s=\frac{3}{5}$$\tan s=\frac{-4}{3}$$\cot s=-\frac{3}{4}$$\sec s=\frac{5}{3}$$\cos ecs=-\frac{5}{4}$