# 7 Chapter Test

Simplify.

1. $\frac{2\text{}{\text{cos}}^{2}\text{}x-\text{cos}\text{}x-1}{\text{cos}\text{}x-1}$

2. ${\left({\displaystyle \frac{\text{sec}\text{}x}{\text{tan}\text{}x}}\right)}^{2}-{\displaystyle \frac{1}{{\text{tan}}^{2}\text{}x}}$

3. Rationalize the denominator:

$$\sqrt{{\displaystyle \frac{1-\text{sin}\text{}\theta}{1+\text{sin}\text{}\theta}}.}$$Assume that the radicand is nonnegative.

4. Given that $x=2\text{}\text{sin}\text{}\theta $, express $\sqrt{4-{x}^{2}}$ as a trigonometric function without radicals. Assume $0<\theta <\pi /2$.

Use the sum or difference identities to evaluate exactly.

5. $\text{sin}\text{}75\xb0$

6. $\text{tan}\text{}{\displaystyle \frac{\pi}{12}}$

7. Assuming that $\text{cos}\text{}u={\displaystyle \frac{5}{13}}$ and $\text{cos}\text{}v={\displaystyle \frac{12}{13}}$ and that $u$ and $v$ are between 0 and $\pi /2$, evaluate $\text{cos}\text{}\left(u-v\right)$ exactly.

8. Given that $\text{cos}\text{}\theta =-{\displaystyle \frac{2}{3}}$ and that the terminal side is in quadrant II, find $\text{cos}\text{}\left(\pi \text{/}2-\theta \right)$.

9. Given that $\text{sin}\text{}\theta =-{\displaystyle \frac{4}{5}}$ and $\theta $ is in quadrant III, find $\text{sin}\text{}2\theta $ and the quadrant in which $2\theta $ lies.

10. Use a half-angle identity to evaluate $\text{cos}\text{}{\displaystyle \frac{\pi}{12}}$ exactly.

11. Given that $\text{sin}\text{}\theta =0.6820$ and that ...

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