Chapter 7 Review

1. Chapter 7 Review

2. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ 2.) if sin θ = ⅔, find cosθ 3.) If cosθ = ¼, find tan θ 4.) If tan θ = 3, find sec θ 5.) if sin θ = 7/10, find cot θ 6.) If tan θ = 7/2, find sin θ ½

3. Express each value as a function of an angle in Quadrant I 1.) sin 458° 2.) cos 892° 3.) tan (-876°) 4.) csc 495° sin 82° -cos 8° tan 24° csc 45°

4. Simplify 1.) 2.) 3.) 4.)

5. Find a numerical value of one trig function. 1.) sin x = 3 cosx 2.) cosx = cot x cscx = 1 Or sin x = 1 tan x = 3

6. Use the sum and difference identities to find the exact value of each function:1.) cos 75° 2.) cos 375° 3.) sin (-165°)4.) sin (-105°) 5.) sin 95° cos 55° + cos 95° sin 55°6.) tan (135° + 120°) 7.) tan 345°

7. If α and β are the measures of two first quadrant angles, find the exact value of each function. 1.) if sin α = 12/13 and cosβ = 3/5, find cos (α – β) 2.) if cosα = 12/13 and cosβ = 12/37, find tan (α – β)

8. If α and β are the measures of two first quadrant angles, find the exact value of each function. 3.) if cosα = 8/17 and tan β = 5/12, find cos (α + β) 4.) if cscα = 13/12 and sec β = 5/3, find sin (α – β)

9. If sin A = 12/13, and A is in the first quadrant, find each value. 1.) cos 2A 2.) sin 2A 3.) tan 2A 4.) cos A/2 5.) sin A/2 6.) tan A/2

10. Use a half-angle identity to find the value of each 1.) 2.) 3.) 4.)

11. Solve for 0° ≤ x ≤ 180° 1.) 2.) 3.) 4.) 30°, 150° No solution, 270° is not in our domain 60° 120°

12. Solve for 0° ≤ x ≤ 180° 1.) 2.) 3.) 4.) 45°, 135° 0° 0°, 180° 0°, 90°, 180°

13. Solve for 0° ≤ x ≤ 180° 1.) 2.) 3.) 4.) 0° 30°, 150° 90° 0°, 135°, 180°

14. Solve for 0° ≤ x ≤ 180° 1.) 2.) 0°, 30°, 150°, 180° 15°, 75°

15. Write each equation in normal form. Then find the measure of the normal, p, and ϕ, the angle that the normal makes with the positive x-axis. 1.) 3x – 2y – 1 = 0 2.) 5x + y – 12 = 0

16. Write each equation in normal form. Then find the measure of the normal, p, and ϕ, the angle that the normal makes with the positive x-axis. 3.) y = x + 5 4.) y = x - 2

17. Write each equation in normal form. Then find the measure of the normal, p, and ϕ, the angle that the normal makes with the positive x-axis. 5.) x + y – 5 = 0 6.) 2x + y – 1 = 0

18. Write the standard form of the equation of the each line given “p”, and ϕ. 1.) p = 4, ϕ = 30° 2.) p = 2, ϕ = 45°

19. Write the standard form of the equation of the each line given “p”, and ϕ. 3.) p = 3, ϕ = 60° 4.) p = 12, ϕ = 120°

20. Write the standard form of the equation of the each line given “p”, and ϕ. 5.) p = 8, ϕ = 150° 2.) p = 15, ϕ = 225°

21. Find the distance between the point with the given coordinates and the line with the given equation. 1.) (-1, 5), 3x – 4y – 1 = 0 2.) (2, 5), 5x – 12y + 1 = 0 3.) (1, -4), 12x + 5y – 3 = 0 4.) (-1,-3), 6x + 8y – 3 = 0

22. Find the distance between each equation. 1.) 2x – 3y + 4 = 0 2.) 4x – y + 1 = 0 y = ⅔x + 5 4x – y – 8 = 0 3.) x + 3y – 4 = 0 4.) 3x – 2y = 6 x + 3y + 20 = 0 3x – 2y + 30 = 0 (0, 4/3) (0, 1) (0, -3) (0, 4/3)

23. Find an equation of the line that bisects the acute angle formed by the graphs of the equations x + 2y - 3 = 0 and x – y + 4 = 0

24. Find an equation of the line that bisects the acute angle formed by the graphs of the equations x + y – 5 = 0 and 2x – y + 7 = 0

25. Find an equation of the line that bisects the acute angle formed by the graphs of the equations 2x + y – 3 = 0 and x – y + 5 = 0