1. Chapter 6 Test Review

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

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

4. y = ±0.75cos(θ – 30°) y = ±4cos(120θ + 3600°)
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 °)

5. Graph: ° ≤ x ≤ 360°, scale 45°
1. y = 2cos (2x – 45°) y = 2sin x + cos x X
2sinx
Cosx
SUM 1 90 2
180 -1
270 -2
360

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
cos x = 1
0°, 360°
cos x =
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) sin (cos-1 ½) cos (sin-1 ½) 4.
1/2
√3/2
√3/2
tan (45° - 45°) = tan 0° = 0

8. Evaluate.

9. State the domain and range of each function:
y = Cos x 2. y = Sin x 3. y = Tan x
4. y = Arccos x 5. y = Sin-1 x 6. y = Arctan x
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 = Arccos x

11. Graph y = Arcsin x

12. Determine a counterexample for the following statement:
1. Cos-1 x = Cos-1 (-x) Sin-1 x = -Sin-1 x
x = 1
x = 1
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, period 6

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.