AnswersS1S-OC Pre-Calculus B E3710 - AGPerformance Task: Trigonometric Identities

Performance Task: Trigonometric Identities — Unit test Answers

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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
2
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A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a point 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?

Question illustration
A
82.3°
B
88.1°
C
93.8°
D
128.0°
3

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))
4

Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of the largest angle in the triangle?

A
52.8°
B
60.0°
C
63.6°
D
82.9°
5

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
6

Which pair of equations below is a result of constructing the altitude, h, in ?

Question illustration
A
sine A = StartFraction h over c EndFraction sine C = StartFraction h over a EndFraction
Option A
B
sine A = StartFraction h over c EndFraction sine B = StartFraction b over c EndFraction
Option B
C
sine A = StartFraction b over c EndFraction sine C = StartFraction b over a EndFraction
Option C
D
sine C = StartFraction h over a EndFraction sine B = StartFraction b over a 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

Jamal draws triangle XYZ. If what is the approximate length of XY?

Question illustration
A
3.4 or 10.4
B
6.4 or 13.7
C
10.4
D
13.7
9

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
10

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
11

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°}
12

Which expression is equivalent to ?

Question illustration
A
tan(x)
B
–tan(x)
C
StartFraction 1 Over cosine (x) EndFraction
Option C
D
Negative StartFraction 1 Over cosine (x) EndFraction
Option D
13

What is the value of 1 − 2sin2(105°)?

A
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option A
B
Negative one-half
Option B
C
One-half
Option C
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option D
14

Which equation could be used to solve for the measure of side q in shown below, given s = 15, S = 45°, and Q = 105°? [Not drawn to scale]

Question illustration
A
StartFraction sine 105 degree over 15 EndFraction = StartFraction sine 30 degree over q EndFraction
Option A
B
StartFraction sine 105 degree over q EndFraction = StartFraction sine 30 degree over 15 EndFraction
Option B
C
StartFraction 15 over sine 105 degree EndFraction = StartFraction q over sine 45 degree EndFraction
Option C
D
StartFraction q over sine 105 degree EndFraction = StartFraction 15 over sine 45 degree EndFraction
Option D
15

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

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