Chapter 6 Test Review

1. Chapter 6 Test Review

2. State the values of θ for which each equation is true: 1.) sin θ = -1 2.) sec θ = -1 3.) tan θ = 0 270° + 360°k 180° + 360°k 180°k 4.) Sin θ = -1 5.) Sec θ = -1 6.) Tan θ = 0 180° 0° -90°

3. State the amplitude, period, and phase shift of each function. • y = -2sin θ 2. y = 10sec θ 3. y = -3sin4θ 4. 5. y = 2.5cos(θ + 180°) 6. A = 2 P = 360° PS = 0° A = 10 P = 360° PS = 0° A = 3 P = 90° or π/2 PS = 0° A = 2.5 P = 360° or 2π PS = 180° π LEFT A = 0.5 P = 360° or 2π PS = 60° π/3 RIGHT A = 1.5 P = 90° or π/2 PS = π/16 RIGHT

4. Write an equation of the cosine function with amplitude, period, and phase shift given. 1. A = 0.75, P = 360°, PS = 30° 2. A = 4, P = 3°, PS = -30° y = ±0.75cos(θ – 30°) y = ±4cos(120θ + 3600°)

5. Graph: -360° ≤ x ≤ 360°, scale 45° 1. y = 2cos (2x – 45°) 2. y = 2sin x + cosx

6. Find the values of x (0°≤x≤360°) that satisfy each equation. 1. x = arccos 1 2. arccos = x 3. arcsin ½ = x 4. sin-1 (-1) = x 5. sin-1 = x 6. cot-1 1 = x cosx = 1 0°, 360° cosx = 45°, 315° sin x = ½ 30°, 150° sin x = -1 270° cot x = 1 45°, 225° sin x = 45°, 135°

7. Evaluate. Assume all angles are in quadrant I • cos (cos-1 ½) 2. sin (cos-1 ½) 3. cos (sin-1 ½) 4. 1/2 √3/2 √3/2 tan (45° - 45°) = tan 0° = 0

8. Evaluate. 1. 2.

9. State the domain and range of each function: • y = Cos x 2. y = Sin x 3. y = Tan x 4. y = Arccosx 5. y = Sin-1x 6. y = Arctanx Domain: 0° ≤ x ≤ 180° Range: -1 ≤ y ≤ 1 Domain: -90° ≤ x ≤ 90° Range: -1 ≤ y ≤ 1 Domain: -90° < x < 90° Range: all reals Domain: -1 ≤ x ≤ 1 Range: 0° ≤ y ≤ 180° Domain: -1 ≤ x ≤ 1 Range: -90° ≤ y ≤ 90° Domain: all reals Range: -90° < y < 90°

10. Graph y = Arccosx

11. Graph y = Arcsinx

12. Determine a counterexample for the following statement: 1. Cos-1x = Cos-1 (-x) 2. Sin-1x = -Sin-1x x = 1 x = 1 3. 4. x = π/2 or 90° x = 0°

13. Find the inverse of each function: 1.) y = Cos (x + π) 2.) y = Sin x 3.) y = Sin θ + π/2 4.) y = Sin (x + π/2)

14. Write an equation with a phase shift 0 to represent a simple harmonic motion under each set of circumstances. 1.) Initial pos. 12, amplitude 12, period 8 2.) Initial pos. 0, amplitude 2, period 8π 3.) Initial pos. -24, amplitude 24, period6

15. The paddle wheel of a boat measures 16 feet in diameter and is revolving at a rate of 20 rpm. If the lowest point of the wheel is 1 foot under water, write an equation in terms of cosine to describe the height of the initial point after “t” seconds.