Algebra and Trigonometry, 5th Edition

Review Exercises

Determine whether the statement is true or false.

1. 1. ${\text{sin}}^{2}s\ne \text{sin}{s}^2$.[7.1]

2. 2. Given $0<\alpha <\pi /2$ and $0<\beta <\pi /2$ and that $\text{sin}\left(\alpha +\beta \right)=1$ and $\text{sin}\left(\alpha -\beta \right)=0$, then $\alpha =\pi /4$.[7.1]

3. 3. If the terminal side of $\theta$ is in quadrant IV, then $\text{tan}\theta <\text{cos}\theta$.[7.1]

4. 4. $\text{cos}5\pi /12=\text{cos}7\pi /12$.[7.2]

5. 5. Given that $\text{sin}\theta =-{\displaystyle \frac{2}{5}},\text{tan}\theta <\text{cos}\theta$.[7.1]

Complete the Pythagorean identity. [7.1]

1. 6. $1+{\text{cot}}^{2}x=$

2. 7. ${\text{sin}}^{2}x+{\text{cos}}^{2}x=$

Multiply and simplify. [7.1]

1. 8. $\left(\text{tan}y-\text{cot}y\right)\left(\text{tan}y+\text{cot}y\right)$

2. 9. ${\left(\text{cos}x+\text{sec}x\right)}^2$

Factor and simplify. [7.1]

1. 10. $\text{sec}x\text{csc}x-{\text{csc}}^{2}x$

2. 11. $3{\text{sin}}^{2}y-7\text{sin}y-20$

3. 12. $1000-{\text{cos}}^{3}u$

Simplify. [7.1]

1. 13. ${\displaystyle \frac{{\text{sec}}^{4}x-{\text{tan}}^{4}x}{{\text{sec}}^{2}x+{\text{tan}}^{2}x}}$

2. 14. ${\displaystyle \frac{2{\text{sin}}^{2}x}{{\text{cos}}^{3}x}}\cdot {\left({\displaystyle \frac{\text{cos}x}{2\text{sin}x}}\right)}^2$

3. 15. ${\displaystyle \frac{3\text{sin}x}{{\text{cos}}^{2}x}}\cdot {\displaystyle \frac{{\text{cos}}^{2}x+\text{cos}x\text{sin}x}{{\text{sin}}^{2}x-{\text{cos}}^{2}x}}$

4. 16. ${\displaystyle \frac{3}{\text{cos}y-\text{sin}y}}-{\displaystyle \frac{2}{{\text{sin}}^{2}y-{\text{cos}}^2}}$