Algebra and Trigonometry, 5th Edition

7 Chapter Test

Simplify.

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

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

3. 3. Rationalize the denominator:

   $$\sqrt{{\displaystyle \frac{1-\text{sin}\theta }{1+\text{sin}\theta }}.}$$

   Assume that the radicand is nonnegative.

4. 4. Given that $x=2\text{sin}\theta$, 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.

1. 5. $\text{sin}75°$

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

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

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

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

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

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