Answer Key
Math 083 Precalc Trig Rewiew
-
University:
Santa Ana College -
Course:
MATH 083 | Beginning and Intermediate Algebra for Liberal Arts and Social Science Academic year:
2020
-
Views:
157
Pages:
7
Author:
Brisa Todd
Name: ________________________
Precalc trig review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A 109 ft tree casts a shadow that is 130 ft long. What is the angle of elevation of the sun?
a. 50°
b. –50°
c. –40°
d. 40°
1 ____
2. Sketch the graph.
1
y = 15sin x
2
a.
d.
b.
e.
c.
2 ____
3. Find the degree measure of the angle:
a.
b.
c.
d.
____
π
15
rad .
12°
6°
16°
27°
4. Choose the value of the trigonometric function cos θ using the information:sin θ =
a.
b.
1
, θ in quadrant I.
5
24
5
No correct answer
−
____
24
5
5. Find the equivalent expression.
____
cot 2 θ + 1
a. cot 2 θ cos 2 θ
b. tan2 θ sin 2 θ
c. tan2 θ sec 2 θ
d. tan2 θ csc 2 θ
e. cot 2 θ sec 2 θ
6. Write the following trigonometric expression in terms of sine and cosine, and then simplify.
____
sin 2 x (1 + cot 2 x)
a. sin x
b. 1
c. cot x
d. cos x
7. Simplify the following trigonometric expression as much as possible.
____
cot x sec x
csc x
a. 1
b. cot x
c. sec x
d. csc x
8. Simplify the following trigonometric expression as much as possible.
c.
1 − cos x
sinx
+
1 − cos x
sinx
a. 2 csc x
b. cos x
c. 2 sin x
d. sin x
3 ____
9. Find the exact value of the expression.
cos −1
a.
b.
c.
d.
e.
π
3
2
3
π
6
0
π
2
1
3
Numeric Response
10. Find the side labeled x. State your answer correct to five decimal places.
x = __________
11. From the top of a 210-ft lighthouse, the angle of depression to a ship in the ocean is 15°.
How far is the ship from the base of the lighthouse? Please round the answer to the nearest foot.
__________ ft
12. Find the exact value of the trigonometric function at the given real number.
csc
3π
2
13. Find the exact value of the trigonometric function at the given real number.
sec(−4π )
4 14. Use a graphing device to find the solutions of the equation, correct to two decimal places.
3 sin x = 2x
x = __________
Short Answer
15. Find the exact value of the expression, if it is defined.
ÊÁ
π ˆ˜
tan−1 ÁÁÁ 2cos ˜˜˜˜
ÁË
3¯
16. Evaluate the expression by sketching a triangle.
ÁÊ
6 ˜ˆ
cot ÁÁÁÁ sin −1 ˜˜˜˜
7¯
Ë
17. Rewrite the expression as an algebraic expression in x.
Ê
ˆ
cos ÁÁ sin −1 x ˜˜
Ë
¯
18. Find all solutions of the equation.
2cos x + 1 = 0
19. Find all solutions of the equation.
tanx sinx + sinx = 0
È
20. Use a double- or half-angle formula to solve the equation in the interval ÍÍÍÎ 0,2π ˆ˜¯ .
tana + cot a = 4sin2a
5 Precalc trig review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
D
A
A
C
E
B
A
A
B
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
NUMERIC RESPONSE
10. ANS: 31.40177
PTS: 1
11. ANS: 784
PTS: 1
12. ANS: -1
PTS: 1
13. ANS: 1
PTS: 1
14. ANS: 1.50
PTS: 1
SHORT ANSWER
15. ANS:
π
4
PTS: 1
16. ANS:
13
6
PTS: 1
1 17. ANS:
1 − x2
PTS: 1
18. ANS:
2π
4π
x=
+ 2k ⋅ π ,
+ 2k ⋅ π
3
3
PTS: 1
19. ANS:
x = k ⋅ π,
3π
+k ⋅π
4
PTS: 1
20. ANS:
π 3π 5π 7π 9π 11π 13π 15π
,
,
,
,
,
,
,
8 8
8
8
8
8
8
8
PTS: 1
2
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Math 083 Precalc Trig Rewiew
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