Chapter 9.3, Problem 13E

To determine

To find: The six trigonometric functions.

Answer to Problem 13E

The six trigonometric functions is calculated.

Explanation of Solution

Given:

The unit circle with $\theta =-270°$ .

Calculation:

The values are,

  $\begin{array}{c}\theta \text{'}=-270°+360°\\ =90°\\ x=0,y=1,r=1\end{array}$

Calculate the trigonometric functions.

  $\begin{array}{c}\sin \theta =\frac{y}{r}\\ =1\\ \cos \theta =\frac{x}{r}\\ =0\end{array}$

  $\begin{array}{c}\tan \theta =\frac{y}{x}\\ =\infty \\ \csc \theta =\frac{r}{y}\\ =1\end{array}$

  $\begin{array}{c}\sec \theta =\frac{r}{x}\\ =\infty \\ \cot \theta =\frac{x}{y}\\ =0\end{array}$

Thus, the six trigonometric functions is calculated.