AnswersPrecalculusTrigonometric Difference Identities

Solving Trigonometric Equations Answers

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1
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What is the exact value of ?

Question illustration
A
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 8 EndFraction
Option A
B
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 4 EndFraction
Option B
C
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 8 EndFraction
Option C
D
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
Option D
2
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Given: < A < and < B < What is tan(A – B)?

Question illustration
A
StartFraction 5 + 12 StartRoot 13 EndRoot Over 12 minus 5 StartRoot 13 EndRoot EndFraction
Option A
B
StartFraction 12 minus 5 StartRoot 13 EndRoot Over 5 + 12 StartRoot 13 EndRoot EndFraction
Option B
C
StartFraction 12 + 5 StartRoot 13 EndRoot Over negative 5 + 12 StartRoot 13 EndRoot EndFraction
Option C
D
StartFraction negative 5 + 12 StartRoot 13 EndRoot Over 12 + 5 StartRoot 13 EndRoot EndFraction
Option D
3

Review the steps of the proof of the identity .Step 1: = Step 2: = Step 3: = Step 4: = Step 5:

Question illustration
A
step 1
B
step 2
C
step 3
D
step 4
4

Review the proof of the identity cos(π − A) = −cosA.cos(π − A)Step 1: = cosπcosA − sinAsinπStep 2: = (−1)(cosA) + (sinA)(0)Step 3: = −1cosA + (sinA)(0)Step 4: = −cosA + 0Step 5: = −cosA

A
step 1
B
step 2
C
step 3
D
step 4
5

What is the value of sin(80°)cos(20°) – cos(80°)sin(20°)?

A
Negative one-half
Option A
B
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option B
C
One-half
Option C
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option D
6

Which values are two of the possible solutions to the equation?

Question illustration
A
Left-brace StartFraction pi Over 20 EndFraction, StartFraction 3 pi Over 20 EndFraction right-brace
Option A
B
Left-brace StartFraction pi Over 4 EndFraction, StartFraction 7 pi Over 4 EndFraction right-brace
Option B
C
Left-brace StartFraction pi Over 4 EndFraction, StartFraction 7 pi Over 20 EndFraction right-brace
Option C
D
Left-brace StartFraction 5 pi Over 4 EndFraction, StartFraction 7 pi Over 4 EndFraction right-brace
Option D
7

Which expression is equivalent to ?

Question illustration
A
Cosine (negative StartFraction pi over 2 EndFraction)
Option A
B
Sine (negative StartFraction pi over 2 EndFraction)
Option B
C
Cosine (StartFraction 2 pi over 3 EndFraction)
Option C
D
Sine (StartFraction 2 pi over 3 EndFraction)
Option D
8

When simplified, is equivalent to which expression?

Question illustration
A
tan(–50°)
B
tan(–30°)
C
tan(30°)
D
tan(50°)
9

Which expression is equivalent to sin(20°)cos(80°) – cos(20°)sin(80°)?

A
sin(–60°)
B
cos(–60°)
C
cos(60°)
D
sin(60°)
10

What is the exact value of ?

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

Which expression is equivalent to cos(40°)cos(10°) + sin(40°)sin(10°)?

A
sin(40° – 10°)
B
cos(40° + 10°)
C
sin(40° + 10°)
D
cos(40° – 10°)
12

Which values represent solutions to , where x [0, 2)?

Question illustration
A
Left-brace 0, pi right-brace
Option A
B
Left-brace 0, StartFraction 3 pi Over 2 EndFraction right-brace
Option B
C
Left-brace StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Option C
D
Left-brace pi, StartFraction 3 pi Over 2 EndFraction
Option D
13

Review the steps of the proof.Step 1: Step 2: Step 3: Step 4:

Question illustration
A
Step 2 should be the last step.
B
Step 3 should be the last step.
C
Steps 2 and 3 must be switched.
D
Steps 3 and 4 must be switched.
14

Review the proof of sin(A – B) = sinAcosB – cosAsinBsin(A – B) = Step 1: Step 2: Step 3: Step 4: = sinAcosB – cosAsinB

Question illustration
A
Step 3 should be step 1.
B
Step 4 should be step 1.
C
Steps 1 and 2 must be switched.
D
Steps 1 and 3 must be switched.
15

Given: cos(3x – 180°) = , where 0 ≤ x < 180°Which values represent the solutions to the equation?

Question illustration
A
{10°, 110°, 130°}
B
{20°, 100°, 140°}
C
{30°, 330°, 390°}
D
{60°, 300°, 420°}

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