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Solving Trigonometric Inequalities Answers

10 verified answers
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 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
3

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
4

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.
5

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
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

Which of the following is part of the solution to the trigonometric inequality over the interval radians?

Question illustration
A
StartFraction pi over 6 EndFraction
Option A
B
StartFraction pi over 2 EndFraction
Option B
C
StartFraction 2 pi over 3 EndFraction
Option C
D
StartFraction 3 pi over 2 EndFraction
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

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
10

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

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