1. Review

2. Find each value by referring to the graphs of the trig functions
sin (-720°)
tan (-180°)
cos (540°)
tan (π)
csc (4π)
sec (π) -1
Undefined -1

3. Find the values of θ for which each equation is true.
sin θ = -1
sec θ = -1
tan θ = 0
sin θ = 0
270° + 360k°
where k is any integer
180° + 360k°
where k is any integer
180k°
where k is any integer
180k°
where k is any integer

4. Graph each function on the given interval.
1.) y = sin x [-90° ≤ x ≤ 90°], scale of 45°

5. Graph each function on the given interval.
1.) y = tan x [-π/2 ≤ x ≤ 3π/2], scale = π/4

6. Graph each function on the given interval.
1.) y = cos x [-360° ≤ x ≤ 360°]

7. Graph each function on the given interval.
1.) y = sec x [-360° ≤ x ≤ 360°]

8. State the amplitude, period, and phase shift for each function.
1.) y = -2sin θ 2.) y = 10sec θ 3.) y = -3sin 4θ 4.) y = 0.5sin (θ- ) 5.) y = 2.5 cos(θ + 180°) 6.) y = -1.5sin (4θ- )
Amp = 2
Per = 360°
PS = 0°
Amp = 10
Per = 360°
PS = 0°
Amp = 3
Per = 90°
PS = 0°
Amp = 0.5
Per = 360°
PS = right
Amp = 2.5
Per = 360°
PS = 180° left
Amp = 1.5
Per = 90°
PS = right

9. Write an equation of the sine function with each amplitude, period, and phase shift
1.) Amp = 0.75, period = 360°, PS = 30° 2.) Amp = 4, period = 3°, PS = -30°
y = ± 0.75 sin(θ- 30°)
y = ± 4 sin(120θ+3600°)

10. Write an equation of the sine function with each amplitude, period, and phase shift
1.) Amp = 0.75, period = 360°, PS = 30° 2.) Amp = 4, period = 3°, PS = -30°
y = ± 3.75 cos (4θ- 16°)
y = ± 12 cos (8θ- 1440)

11. Graph each function:
1.) y = 0.5 sin x

12. Graph each function:
1.) y = 2 cos (3x)

13. Graph each function:
1.) y = 2 cos (2x – 45°)

14. Graph each function:
1.) y = tan (x + 60°)

15. Find the exact value of each expression without using a calculator
Find the exact value of each expression without using a calculator. When your answer is an angle, express it in radians. Work out the answers yourself before you click.

16. Answers for problems 1 – 9.
Negative ratios for arccos generate angles in Quadrant II. y x 1 2
The reference angle is
so the answer is

17. y x -1 2
14. x 1 2 y
15.

18. Graph each function:
1.) y = -2cos (3θ), scale π/4, -2π ≤ θ ≤ 2π

19. Graph each function:
1.) y = ½ cos(x – π/2)

20. Find the values of x in the interval 0 ≤x ≤ 2π that satisfies the equation:

21. Evaluate each expression. Assume all angles are in Quadrant I

22. Quick Quiz Find the values of θ for which the equation
tan θ = 1 is true.
State the domain and range for the function
y = -csc x
State the amplitude, period, and phase shift of:
Write an equation of the cosine function with
amplitude 7, period π, and phase shift 3π/2
45°+180°k
D = all reals except 180°k
R = y ≤ -1 or y ≥ 1
A = ⅓ PS = -π/6
P = 2π