AnswersPrecalculusSolving Trigonometric Inequalities

Solving Trigonometric Inequalities — Unit test Answers

15 verified answers2 views
1
Free Preview

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
Free Preview

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
3

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
4

What is the exact value of tan ?

Question illustration
A
Negative 2 minus StartRoot 3 EndRoot
Option A
B
Negative 2 + StartRoot 3 EndRoot
Option B
C
1 minus StartRoot 3 EndRoot
Option C
D
1 + StartRoot 3 EndRoot
Option D
5

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°}
6

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
7

Which shows a correct simplification of sin(x + )?

Question illustration
A
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · 1 + cos(x) · 0= sin(x)
Option A
B
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · 1 – sin(x) · 0= cos(x)
Option B
C
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · –1 + cos(x) · 0= –sin(x)
Option C
D
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · –1 – sin(x) · 0= –cos(x)
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

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
10

Which function is equivalent to the inverse of ?

Question illustration
A
mc020-2.jpg
Option A
B
mc020-3.jpg
Option B
C
mc020-4.jpg
Option C
D
mc020-5.jpg
Option D
11

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

Question illustration
A
0 is less than equal to x and x is less than StartFraction pi over 4 EndFraction
Option A
B
and
Option B
C
x is greater than StartFraction pi over 4 EndFraction but less than StartFraction 5pi over 4 EndFraction
Option C
D
and
Option D
12

Review the diagram of the unit circle.

Question illustration
A
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus 1) squared minus (sine (u) minus 0) squared EndRoot
Option A
B
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (negative v) minus 1) squared + (sine (negative v) minus 0) squared EndRoot
Option B
C
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus cosine (negative v) ) squared + (sine (u) minus sine (negative v)) squared
Option C
D
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u + v) minus cosine (u) ) squared + (sine (u + v) minus sine (u)) squared EndRoot
Option D
13

Read the proof.

Question illustration
A
tangent double angle identity
Option A
B
tangent sum identity
Option B
C
tangent double angle identity
Option C
D
tangent sum identity
Option D
14

To solve the trigonometric inequality over the interval radians, Gabby performed the following steps, first simplifying the inequality and then setting both sides equal to y and graphing the equations. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: In which step did she first make an error, and what was the error?

Question illustration
A
She first made an error in step 3 because she should not have subtracted and added to the right side of the inequality.
Option A
B
She first made an error in step 4 because the simplified form of the inequality should have been instead of .
Option B
C
She first made an error in step 5 because she did not correctly graph .
Option C
D
She first made an error in step 6 because she chose the wrong interval in which the graph of one equation is at or above the graph of the other equation.
15

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))

Did you find these answers helpful?

More from this Course

Quiz
14 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test