Honors Pre-Calculus Review: Unit 5
Name: __________________________
Multiple Choice: Choose the best answer to each question. Place your final answer on the answer line provided. No
partial credit is given.
1. A simpler expression for (sec θ + 1)(sec θ – 1) is ______________.
a. cos2θ
b. cot2θ
c. sec2θ
2. Which of these is an efficient first step in proving the identity
sin x
1 cos x
sin x
b.
1 cos x
sin x
c.
1 cos x
a.
cos
x
2
1 cos x
sin x
2
sin x cos 2 x cos x
sin x csc x
1 cos x csc x
1. ___________
2
d. tan θ
e. sin2θ
sin x
1 cos x
1 cos x
?
sin x
sin x
sin x
d.
1 cos x 1 cos x
sin x
sin x
e.
1 cos x 1 cos x
2. ___________
1
1
1
1
cos x
cos x
cos x
cos x
3. How many numbers between 0 and 2π solve the equation 3 cos2x + cos x = 2?
a. 0
d. 3
b. 1
e. 4
c. 2
3. ___________
4. What is the exact value of sin 15°?
4. ___________
a.
b.
c.
1
4
d.
3
4
e.
3
6
2
4
6
2
4
2
4
5. Which expression is equivalent to cos 47° cos 23° - sin 47° sin 23°?
a. cos 70°
d. sin 24°
b. sin 70°
e. tan 70°
c. cos 24°
5. ___________
6. What is the exact value of sin 22.5°?
6. ___________
a.
2
4
d.
b.
3
4
e.
c.
2
6
2
4
2
2
2
2
2
7. Which expression is equivalent to sin 32°cos 21° - sin 21°cos 32°?
a.
sin 53°
b.
sin 11°
7. ___________
c. cos 53°
d. cos 11°
e. sin 32°
8. The shortest side of a triangle with angles 50°, 60°, and 70° has length 9. What is the
length of the longest side?
a. 11
d. 12.5
b. 11.5
e. 13
c. 12
8. ___________
9. In ∆ABC, ∠A = 95°, ∠B = 53°, and c = 12. Find b.
a. 8.6
b. 15
c. 18.1
9. _____________
10. The area of a triangle with sides 7, 8, and 9 is...
a.
6 15
b. 12 5
c.
16 3
d. 17 3
e. 18 3
d. 19.2
e. 22.6
10.__________
Open Response: Show your work on each question. Place your final answer on the answer line provided. Partial
credit can be earned through relevant, correct work with minor errors.
11. Solve for each missing value in this triangle. If needed, round to the nearest tenth.
11. ________________
12. Find the area of the triangle below. Round to the nearest tenth.
12. ________________
13. Write
sin 2 x
as an algebraic expression of a single trigonometric function.
1 cos x
14. Find all solutions to cos 2x = cos x in the interval [0, 2π).
13._________________
14. ________________
15. Find sec θ and csc θ if tan θ = 4 and cos θ < 0.
15._________________
16. Solve for each missing value in this triangle. If needed, round to the nearest tenth.
16._________________
17. Use a sum or difference identity to find an exact value of cos
17. ________________
12
.
18. Simplify the expression into an expression involving 1 trigonmetric function.
(sec x 1)(sec x 1)
sin 2 x
18. ________________