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Solving Trigonometric Inequalities Answers

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1
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To help solve the trigonometric inequality , which two equations could you graph?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
2
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Which of the following is part of the solution to the trigonometric inequality over the interval radians?

Question illustration
A
x is equal to StartFraction pi over 6 EndFraction
Option A
B
x is equal to StartFraction pi over 3 EndFraction
Option B
C
x is equal to StartFraction 2pi over 3 EndFraction
Option C
D
x is equal to StartFraction 5pi over 6 EndFraction
Option D
3

To solve the trigonometric inequality , Carl graphed the equations and . Shelly, on the other hand, took the cube root of both sides of the inequality so that it became , and she then graphed the equations and . Which of the following statements is true regarding the points of intersection of Carl’s graph and Shelly’s graph?

Question illustration
A
The points of intersection of Carl’s graph have different x-coordinates than the points of intersection of Shelly’s graph and different y-coordinates.
B
The points of intersection of Carl’s graph have different x-coordinates than the points of intersection of Shelly’s graph but the same y-coordinates.
C
The points of intersection of Carl’s graph have the same x-coordinates as the points of intersection of Shelly’s graph but different y-coordinates.
D
The points of intersection of Carl’s graph have the same x-coordinates as the points of intersection of Shelly’s graph and the same y-coordinates.
4

The graph below can be used to help solve which of the following trigonometric inequalities over the interval radians?

Question illustration
A
cosine (x) is greater than equal to minus 1
Option A
B
cosine (x) minus sine (x) is greater than equal to minus 1
Option B
C
sine (x) is greater than equal to minus 1
Option C
D
sine (x) minus cosine (x) is greater than equal to minus 1
Option D
5

In which of the following intervals does the trigonometric inequality always hold true?

Question illustration
A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
6

Which of the following trigonometric inequalities has no solution over the interval radians?

Question illustration
A
cosine (x) is less than 1
Option A
B
cosine (StartFraction x over 2 EndFraction) is less than 1
Option B
C
cosecant (x) is less than 1
Option C
D
cosecant (StartFraction x over 2 EndFraction) is less than 1
Option D
7

What is the solution to the trigonometric inequality over the interval radians?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
8

To help solve the trigonometric inequality , which two equations can be graphed?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
9

The graph below can be used to help solve which of the following trigonometric inequalities over the interval radians?

Question illustration
A
5 cosine (x) minus 7.5 is greater than equal to 6 cosine (x) minus 7
Option A
B
5 sine (x) minus 7.5 is greater than equal to 6 sine (x)minus 7
Option B
C
5 sine (x) minus 7 is greater than equal to 6 cosine (x) minus 7.5
Option C
D
5 sine (x) minus 7 is greater than equal to 6 sine (x) minus 7.5
Option D
10

Which quarters of the unit circle satisfy the trigonometric inequality ? Assume that is the angle made by the positive x-axis and a ray from the origin.

Question illustration
A
the top right and bottom right quarters
B
the top right and bottom left quarters
C
the top left and bottom right quarters
D
the top left and bottom left quarters

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