AnswersPrecalculusSolving Trigonometric Inequalities

Solving Trigonometric Inequalities Answers

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Which half of the unit circle satisfies 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 half
B
the bottom half
C
the right half
D
the left half
2
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Which trigonometric inequality has no solution over the interval radians?

Question illustration
A
cosecant (x) minus 1 is greater than 0
B
cosine (x) minus 1 is greater than 0
C
cotangent (x) minus 1 is greater than 0
D
tangent (x) minus 1 is greater than 0
3

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
4

To help solve the trigonometric inequality , Tracey successfully graphed the equations and with her graphing calculator. Which of the following statements is true about the inequality?

Question illustration
A
There is no solution because even though you cannot see it, the graph of the equation is above the graph of the equation for all values of x.
B
There is no solution because the graph of the equation is the same as the graph of the equation , so is never below .
C
There are an infinite number of solutions because even though you cannot see it, the graph of the equation is below the graph of the equation for all values of x.
D
There are an infinite number of solutions because the graph of the equation is the same as the graph of the equation , so is never below .
5

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

Question illustration
A
sine (x) minus 1 is less than equal to cosine (2x) minus 2
Option A
B
sine (x) minus 1 is less than equal to cosine (2x) plus 2
Option B
C
sine (2x) minus 1 is less than equal to cosine (x) minus 2
Option C
D
sine (2x) minus 1 is less than equal to cosine (x) plus 2
Option D
6

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
7

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
8

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
9

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
10

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.
11

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
12

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
13

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
14

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
15

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

Question illustration
A
all of the unit circle
B
the top half of the unit circle
C
the right half of the unit circle
D
none of the unit circle

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