Chapter 6 Summary and Review
Study Guide
KEY TERMS AND CONCEPTS  EXAMPLES 

SECTION 6.1: TRIGONOMETRIC FUNCTIONS OF ACUTE ANGLES  
Trigonometric Function Values of an Acute Angle $\theta $ Let $\theta $ be an acute angle of a right triangle. The six trigonometric functions of $\theta $ are as follows: $$\begin{array}{cc}\text{sin}\text{}\theta \text{}={\displaystyle \frac{\text{opp}}{\text{hyp}}}\text{,}\hfill & \text{csc}\text{}\theta ={\displaystyle \frac{\text{hyp}}{\text{opp}}}\text{,}\hfill \\ \text{cos}\text{}\theta ={\displaystyle \frac{\text{adj}}{\text{hyp}}}\text{,}\hfill & \text{sec}\text{}\theta \text{}={\displaystyle \frac{\text{hyp}}{\text{adj}}}\text{,}\hfill \\ \text{tan}\text{}\theta \text{}={\displaystyle \frac{\text{opp}}{\text{adj}}}\text{,}\hfill & \text{cot}\text{}\theta ={\displaystyle \frac{\text{adj}}{\text{opp}}}\text{.}\hfill \end{array}$$

If $\text{cos}\text{}\alpha ={\displaystyle \frac{3}{8}}$ and $\alpha $ is an acute angle, find the other five trigonometric function values of $\alpha $. We find the missing length using the Pythagorean equation: ${a}^{2}+{b}^{2}={c}^{2}$.
$\begin{array}{c}\begin{array}{ccc}\hfill {a}^{2}+{3}^{2}& =\hfill & {8}^{2}\hfill \end{array}\end{array}$ 
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