Practice Exam 1 - Chapter 4
Name:
Instructions:
Give yourself 50 minutes to complete this practice exam.
Justify each answer.
Record your answer in the answer fields.
Each answer has equal weight.
1.
10.
2.
11.
3.
12.
4.
13.
5.
14.
6.
15.
7.
16.
8.
17.
9.
18.
==============================
19. Period =
Amplitude =
Phase =
20.
sin(θ)
cos(θ)
tan(θ)
1
−π
−2π
1
π
2π
−π
−2π
−1
2π
sec(θ)
−π
−2π
−π
π
2π
−π
π
2π
−1
csc(θ)
−2π
π
π
2π
−2π
cot(θ)
−π
π
2π
−2π
21.
arcsin(θ)
−1
arccos(θ)
arctan(θ)
π
π
π
π
2
π
2
π
2
−1/2
1/2
1
−1
−1/2
1/2
1
- π2
- π2
- π2
-π
-π
-π
π
22. f (θ) = 3 cos θ +
8
4
3
2
1
−2π
− 3π
2
−π
− π2
π
2
−1
−2
−3
−4
π
3π
2
2π
12π
1. Suppose θ =
radians. Find two coterminal angles, one positive
5
and one negative.
2. Suppose θ = −
3π
radians. Convert the angle to degrees.
8
3. A disc with radius 3 cm spins 40 revolutions per minute. Give the
angular speed in radians per minute and the linear speed in cm per
minute.
For #4 to #9, use the picture below.
5
1
−√ , √
26
26
θ
What are the values for the six trigonometric functions for this θ.
4. sin(θ) =
5. cos(θ) =
6. tan(θ) =
7. csc(θ) =
8. sec(θ) =
9. cot(θ) =
For #10 to #14, suppose tan(θ) =
5
and sin(θ) > 0.
3
What are the other five trigonometric function values for this θ?
10. sin(θ) =
11. cos(θ) =
12. csc(θ) =
13. sec(θ) =
14. cot(θ) =
15. Suppose that θ = 215◦ . What number is the reference angle in degrees?
16. In which of the four quadrants does θ lie when sin(θ) < 0 and
tan(θ) < 0 ?
1
17. Suppose cos(θ) = − . What are two different numbers for θ between
2
0◦ and 360◦ ?
18. What is the exact value of
3
cot arcsin
?
8
19. Find the period, amplitude, and phase of the function f (x) = a sin (bx + c)
graphed below.
3
2
1
−4π
−3π
−2π
−π
π
2π
3π
4π
π
2
π
3π
2
2π
−1
−2
−3
20. Sketch a graph of sin, cos, tan, csc, sec, cot.
21. Sketch a graph of arcsin, arccos, arctan.
π
.
22. Sketch a graph for f (θ) = 3 cos θ +
8
4
3
2
1
−2π
− 3π
2
−π
− π2
−1
−2
−3
−4