AnswersPrecalculusTrigonometric Sum Identities

Trigonometric Sum Identities — Cumulative exam Answers

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1
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What is the exact value of sin(105°)?

A
Negative StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option A
B
Negative StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option B
C
StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option C
D
StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option D
2
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What are the coefficients for the binomial expansion of (a + b)3?

A
1, 4, 6, 4, 1
B
1, 1
C
1, 2, 1
D
1, 3, 3, 1
3

Consider the function.f(x) = x2 + 3Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?

A
f(x) domain: x ≥ 3f–1(x) domain: x ≥ 3
B
f(x) domain: x ≥ 3f–1(x) range: y ≥ 3
C
f(x) domain: x ≥ 0f–1(x) domain: x ≥ 0
D
f(x) domain: x ≥ 0f–1(x) range: y ≥ 0
4

What is the solution of ?

Question illustration
A
–1 < x < 1 or
Option A
B
–1 < x < 1 or
Option B
C
x < –1 or
Option C
D
x < –1 or
Option D
5

What is the amplitude of the cosine function corresponding to the secant function graphed below?

Question illustration
A
–2
B
–1
C
2
D
3
6

Review the proof.

Question illustration
A
1 – cos(x)
B
1 + cos(x)
C
StartRoot 1 minus cosine (x) EndRoot
Option C
D
StartRoot 1 + cosine (x) EndRoot
Option D
7

Which graph represents ?

Question illustration
A
On a coordinate plane, a function has a maximum of 6 and minimum of 4. It completes one period at pi. It crosses the y-axis at (0, 4).
Option A
B
On a coordinate plane, a function has a maximum of 6 and minimum of 4. It completes one period at pi. It decreases through the y-axis at (0, 5).
Option B
C
On a coordinate plane, a function has a maximum of 7 and minimum of 3. It completes one period at 2 pi. It crosses the y-axis at (0, 3).
Option C
D
On a coordinate plane, a function has a maximum of 7 and minimum of 3. It completes one period at 2 pi. It decreases through the y-axis at (0, 5).
Option D
8

A polynomial function has a root of –6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

A
mc014-1.jpg
Option A
B
mc014-2.jpg
Option B
C
mc014-3.jpg
Option C
D
mc014-4.jpg
Option D
9

The function h(x) = –x5 + 12x is an odd function. Which transformation of h(x) results in an odd function?

A
h(5 – x)
B
1 + h(x)
C
h(x + 8)
D
–6h(x)
10

Which statement about the simplified binomial expansion of (a + b2)n, where n is a positive integer, is true?

A
The exponent of b will always be even.
B
The exponent of a will always be odd.
C
The sum of the exponents of a and b will always equal n.
D
The sum of the exponents of a and b will always equal n – 1.
11

A disc spins at a rate of 6.4 revolutions per minute. To the nearest tenth, what is the linear velocity, in meters per minute, of a point on the disc that is 3 cm from the center of the disc? m/min

Answer not available
12

Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?

Question illustration
A
The oblique asymptote for g(x) is steeper than for f(x).
B
Both functions have the same oblique asymptote.
C
The oblique asymptote for f(x) is steeper than for g(x).
D
Both functions have parallel oblique asymptotes.
13

What is the solution of ?

Question illustration
A
6
B
9
C
18
D
81
14

What is the solution to 4x 3 – 3x 2 – 7x < 0?

A
(–ꝏ, –1) U (0, 1.75)
B
(–ꝏ, –1] U [0, 1.75]
C
(–1, 0) U (1.75, ꝏ)
D
[–1, 0] U [1.75, ꝏ)
15

What restriction should be applied to y = tanx for y = arctanx to be defined?

A
Restrict the range to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option A
B
Restrict the range to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option B
C
Restrict the domain to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option C
D
Restrict the domain to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option D
16

Earth revolves on its axis once every 24 hours. Which statements are true? Check all that apply.The angular velocity of Earth is π/12 radians per hour. The angular velocity of Earth is π/12 radians per day. The angular velocity of Earth is 2π radians per hour.The angular velocity of Earth is 2π radians per day. The angular velocity of Earth is 12π radians per day.

A
The angular velocity of Earth is π/12 radians per hour.
B
The angular velocity of Earth is π/12 radians per day.
C
The angular velocity of Earth is 2π radians per hour.
D
The angular velocity of Earth is 2π radians per day.
E
The angular velocity of Earth is 12π radians per day.
17

Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $300. The store allows the coupons to be combined. Which coupon should be applied first, and what is the final purchase price?

A
Apply the 15% discount first, and the final purchase price is $332.50.
B
Apply the 15% discount first, and the final purchase price is $340.00.
C
Apply the $50 off first, and the final purchase price is $332.50.
D
Apply the $50 off first, and the final purchase price is $340.00.
18

Study the graphs of f(x) and g(x).

Question illustration
A
Vertical stretch followed by a translation 1 unit left, so g(x) = f.
Option A
B
Vertical stretch followed by a translation 1 unit right, so g(x) = f.
Option B
C
Horizontal stretch followed by a translation 1 unit left, so g(x) = f.
Option C
D
Horizontal stretch followed by a translation 1 unit right, so g(x) = f.
Option D
19

Which term, when added to the given polynomial, will change the end behavior of the graph? y = 14x8 – 6x5 – 2x4 – 10

A
–6x9
B
–5x7
C
5x8
D
6x10
20

Suppose . Which value(s) of a would make the composite functions commutative?

Question illustration
A
0
B
2
C
any value of a
D
no value of a

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