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MAC 1114 Module Test 5
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express the given trigonometric function in terms of the indicated function.
1) cot θ in terms of cos θ
2
A) ±cos θ 1 - cos θ
1 - cos2 θ
C) ±
B) ±
1 - cos2 θ
cos θ
D)
1 + cos2 θ
cos θ
1
cos θ
Answer: A
Objective: (5.1) Find Trig Function in Terms of Other Trig Functions
Use the fundamental identities to find the value of the trigonometric function.
2) Find sin θ if cot θ = - 5 and cos θ < 0.
A) - 26
B)
26
26
C)
26
5
D) - 1
5
Answer: B
Objective: (5.1) Find Other Trig Function Values Given One Value, Quadrant
Complete the sentence so the result is an identity. Let x be any real number.
3)
= 1
sin x
A) cot x
B) sec x
C) tan x
D) csc x
C) tan x
D) csc x
Answer: D
Objective: (5.1) Complete Identity Equation
4) cos x = (cot x)(
A) sin x
)
B) sec x
Answer: A
Objective: (5.1) Complete Identity Equation
Show that the equation is not an identity by listing the value(s) of the variable from among 0, π , π , and - π for
4 2
4
which the equation is false.
5) sin2θ = cos2θ
A) - π
4
B) π and - π
4
4
C) 0 and π
2
Answer: C
Objective: (5.1) Tech: Show That Equation is Not Identity
1
D) π
2
6) (sin θ + cos θ)2 = 1
A) π
2
B) - π
4
C) 0 and π
2
D) π and - π
4
4
C) - π
4
D) π
2
C) π , π , and - π
4 2
4
D) π and - π
4
4
C) sec2θ
D) 1
C) csc2 x
D) csc x
Answer: D
Objective: (5.1) Tech: Show That Equation is Not Identity
7)
sin θ + cos θ = 1
A) π and - π
4
4
B) 0 and π
2
Answer: A
Objective: (5.1) Tech: Show That Equation is Not Identity
8) (tan θ + 1)2 = sec2 θ
A) π and 0
2
B) π , π , and 0
4 2
Answer: C
Objective: (5.1) Tech: Show That Equation is Not Identity
Use the fundamental identities to simplify the expression.
9) 1 + sec θ cos θ
cot2θ
A) csc2θ
B) tan2θ
Answer: C
Objective: (5.2) Simplify Trigonometric Expression I
Simplify the expression.
2
10) cos x + cos x sec x
sin2 x
A) sec2 x
B) cot2 x
Answer: C
Objective: (5.2) Simplify Trigonometric Expression II
Decide whether the expression is or is not an identity.
11) tan t cot t = 1
A) Identity
B) Not an identity
Answer: A
Objective: (5.2) Verify if Trig Equation is Identity I (Y/N)
Perform the indicated operations and simplify the result.
2
12) (sin θ + cos θ)
1 + 2 sin θ cos θ
A) 1
C) 1 - sin θ
B) 0
Answer: A
Objective: (5.2) Perform Indicated Operation
2
D) - sec2θ
Identify the equation as either an identity or not.
13) tan2x = sec2x - sin2x - cos2x
A) Not an identity
B) Identity
Answer: B
Objective: (5.2) Verify if Trig Equation is Identity II (Y/N)
Find the exact value of the expression using the provided information.
14) Find cos(A - B) given that cos A =
A)
37 - 6
74
111
B) -
37 , with A in quadrant I, and sin B = 37
37
74
C)
37 73
2
3 , with B in quadrant IV.
111
D)
37 + 6
74
111
Answer: A
Objective: (5.3) Use Cosine Sum and Difference Identities
Use the cofunction identities to find an angle θ that makes the statement true.
15) sin (5θ + 12°) = cos (2θ - 5°)
A) θ = 17°
B) θ = 40°
C) θ = 83°
7
7
D) θ = 10°
Answer: C
Objective: (5.3) Find Angle to Obtain True Statement
16) sin (θ + 4°) = cos (θ + 6°)
A) θ = 17°
7
B) θ = 83°
7
C) θ = 40°
D) θ = 10°
C) tan 52.453°
D) tan (-52.453°)
Answer: C
Objective: (5.3) Find Angle to Obtain True Statement
Write in terms of the cofunction of a complementary angle.
17) cot 142.453°
A) tan 37.547°
B) cot 37.547°
Answer: D
Objective: (5.3) Change to Cofunction of Complementary Angle
Use the cofunction identities to find an angle θ that makes the statement true.
18) sin (3θ - 17°) = cos (θ + 43°)
A) θ = 6°
B) θ = 10°
C) θ = 16°
D) θ = 90°
Answer: C
Objective: (5.3) Find Angle to Obtain True Statement
Find the exact value of the expression using the provided information.
19) Find cos(A - B) given that sin A = A)
186 +
18
15
B)
3
3 , with A in quadrant IV, and sin B = -
186 18
15
C)
Answer: A
Objective: (5.3) Use Cosine Sum and Difference Identities
3
55 18
15
6
5 , with B in quadrant IV.
D)
55 +
18
15
Use an appropriate identity to find the exact value of the expression.
20) cos 5π
12
A) -
3 + 1)
2(
4
B)
3 - 1)
2(
C)
4
Answer: B
Objective: (5.3) Find Exact Value of Expression (Radians)
4
3 + 1)
2(
4
D) -
3 - 1)
2(
4