1. Chapter 7 Review

2. Solve for 0° ≤ θ ≤ 90°. 1. ) If tan θ = 2, find cot θ. 2
Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ 2.) if sin θ = ⅔, find cos θ
  3.) If cos θ = 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

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.) )
  3.) )

5. Find a numerical value of one trig function.
1.) sin x = 3 cos x 2.) cos x = cot x
csc x = 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° ) cos 375° 3.) sin (-165°) ) sin (-105°) 5.) sin 95° cos 55° + cos 95° sin 55° ) 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 cos β = 3/5,
find cos (α – β)
2.) if cos α = 12/13 and cos β = 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 cos α = 8/17 and tan β = 5/12, find cos (α + β)
4.) if csc α = 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/ ) tan A/2

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

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

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

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

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

15. Write each equation in normal form
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 = ) 5x + y – 12 = 0

16. Write each equation in normal form
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 ) y = x - 2

17. Write each equation in normal form
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 = ) 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 = ) 4x – y + 1 = 0
y = ⅔x x – y – 8 = 0
3.) x + 3y – 4 = ) 3x – 2y = 6
x + 3y + 20 = x – 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