AnswersPrecalculusSolving Trigonometric Inequalities

Solving Trigonometric Inequalities — Unit test Answers

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For what values of x is the trigonometric equation tan(x − 180°) − sin(x − 180°) = 0, where 0 ≤ x < 360°, true?

A
{0°, 90°}
B
{0°, 180°}
C
{90°, 180°}
D
{90°, 270°}
2
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Which is the graph of ?

Question illustration
A
A smooth curve resembling an arctangent function. The x-axis ranges from -6 to 6, and the y-axis from -p to p. The curve approaches horizontal asymptotes at y = p/2 and y = -p/2, passing through the origin.
Option A
B
A graph of a function with asymptotic behavior. The x-axis ranges from -5 to 5, and the y-axis ranges from -p to p. The curve is located in the fourth quadrant, approaching the y-axis asymptotically as x approaches zero from both positive and negative directions. The curve also approaches zero asymptotically as x moves away from zero in both directions. The function does not intersect either axis.
Option B
C
A graph of a function with the x-axis ranging from -2.5 to 2.5 and the y-axis ranging from -p to p. The curve passes through the origin (0,0) and changes direction at y=0. It intersects the x-axis at two points, approximately at x=-1 and x=1. The curve is symmetric about the origin.
Option C
D
The image shows a mathematical graph plotted on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -p to p. A smooth, continuous curve intersects the x-axis at approximately 1. The curve extends into both the positive and negative quadrants. The point p is labeled on the positive y-axis and -p on the negative y-axis.
Option D
3

What are the solutions to the equation over the interval [0, 2]?

Question illustration
A
only
Option A
B
only
Option B
C
only
Option C
D
StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 7 pi Over 6 EndFraction and StartFraction 11 pi Over 6 EndFraction
Option D
4

The motion of a weight that hangs from a spring is represented by the equation . It models the weight’s height, h, in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 4 inches below the rest position? Round to the nearest hundredth, if necessary.

Question illustration
A
0 seconds
B
0.29 seconds
C
0.39 seconds
D
1.95 seconds
5

Which statement is true about the graph of the equation ?

Question illustration
A
There is a horizontal asymptote at .
Option A
B
There is a horizontal asymptote at .
Option B
C
There is a vertical asymptote at .
Option C
D
There is a vertical asymptote at .
Option D
6

Which function is equivalent to the inverse of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

Which expression is equivalent to ?

Question illustration
A
tan(x)
B
–tan(x)
C
StartFraction 1 Over cosine (x) EndFraction
Option C
D
Negative StartFraction 1 Over cosine (x) EndFraction
Option D
8

Which expression is equivalent to ?

Question illustration
A
Cosine (negative StartFraction pi Over 3 EndFraction)
Option A
B
Sine (negative StartFraction pi Over 3 EndFraction)
Option B
C
Cosine (StartFraction pi Over 2 EndFraction)
Option C
D
Sine (StartFraction pi Over 2 EndFraction)
Option D
9

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
10

What is the exact value of tan(195°)?

A
StartFraction StartRoot 3 EndRoot + 1 Over 1 minus StartRoot 3 EndRoot EndFraction
Option A
B
StartFraction StartRoot 3 EndRoot minus 3 Over 3 + StartRoot 3 EndRoot EndFraction
Option B
C
StartFraction StartRoot 3 EndRoot minus 1 Over 1 + StartRoot 3 EndRoot EndFraction
Option C
D
StartFraction StartRoot 3 EndRoot + 3 Over 3 minus StartRoot 3 EndRoot EndFraction
Option D
11

Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?

A
30° only
B
90° only
C
30° or 150°
D
30°, 90°, or 150°
12

For , which expression is equivalent to ?

Question illustration
A
StartFraction 1 Over StartRoot 2 (1 + cosine x) EndRoot EndFraction
Option A
B
StartFraction 1 Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction
Option B
C
(StartRoot StartFraction 1 + cosine (x) Over 2 EndFraction EndRoot) (StartFraction 1 Over 1 minus cosine (x) EndFraction)
Option C
D
(StartFraction 1 + cosine (x) Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction) (StartFraction 1 Over 1 minus cosine (x) EndFraction)
Option D
13

Review the proof of cos(A - B) = cosAcosB + sinAsinB.Step 1: Step 2: Step 3: Step 4: Step 5:Step 6:Step 7:

Question illustration
A
1 and 1
B
2 and 1
C
(cosAcosB)2(sinAsinB)2 and (cos2(A – B))((sin2(A – B))
D
(cos2A + sin2A)(cos2B + sin2B) and (cos2(A – B))(sin2(A – B))

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