AnswersSS26 Math 3 S2 M3960OXGraphing Tangent and Cotangent

Trigonometric Inverses and Their Graphs Answers

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What is the equation of the graph below?

Question illustration
A
y = sec(x) + 2
B
y = csc(x) + 2
C
y = csc(x + 2)
D
y = sec(x + 2)
2
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What is the equation of the graph below?

Question illustration
A
y = sine (x + 90 degrees)
Option A
B
y = cosine (x + 90 degrees)
Option B
C
y = sine (x + 45 degrees)
Option C
D
y = cosine (x + 45 degrees)
Option D
3

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

A
It is the graph of y = sec(x) shifted 3 units right and 7 units up.
B
It is the graph of y = sec(x) shifted 3 units left and 7 units up.
C
It is the graph of y = sec(x) shifted 3 units left and 7 units down.
D
It is the graph of y = sec(x) shifted 3 units right and 7 units down.
4

Which of the following could be the equation of the function below?

Question illustration
A
y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2
Option A
B
y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2
Option B
C
y = 0.5 cosine (4 (x + pi)) + 2
Option C
D
y = 0.5 cosine (2 (x minus pi)) minus 2
Option D
5

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

Question illustration
A
31 square inches
B
34 square inches
C
48 square inches
D
62 square inches
6

Which is an x-intercept of the graph of the function ?

Question illustration
A
(minus StartFraction 2pi over 3 EndFraction , 0)
Option A
B
(minus StartFraction pi over 3 EndFraction , 0)
Option B
C
(StartFraction pi over 6 EndFraction , 0)
Option C
D
(StartFraction 5pi over 6 EndFraction , 0)
Option D
7

Two teams are pulling a heavy chest, located at point X. The teams are 4.6 meters away from each other. Team A is 2.4 meters away from the chest, and Team B is 3.2 meters away. Their ropes are attached at an angle of 110°.Law of sines:

Question illustration
A
StartFraction sine (uppercase A) Over 2.4 EndFraction = StartFraction sine (110 degrees) Over 4.6 EndFraction
Option A
B
StartFraction sine (uppercase A) Over 4.6 EndFraction = StartFraction sine (110 degrees) Over 2.4 EndFraction
Option B
C
StartFraction sine (uppercase A) Over 3.2 EndFraction = StartFraction sine (110 degrees) Over 4.6 EndFraction
Option C
D
StartFraction sine (uppercase A) Over 4.6 EndFraction = StartFraction sine (110 degrees) Over 3.2 EndFraction
Option D
8

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
9

Which of the following is true of the location of an angle, , whose tangent value is ?

Question illustration
A
has a 30-degree reference angle and is located in Quadrant II or IV
Option A
B
has a 30-degree reference angle and is located in Quadrant II or III
Option B
C
has a 60-degree reference angle and is located in Quadrant II or IV
Option C
D
has a 60-degree reference angle and is located in Quadrant II or III
Option D
10

Which of the following could be the measure of the angle below?

Question illustration
A
–180°
B
–120°
C
140°
D
510°
11

Which function will have a y-intercept at –1 and an amplitude of 2?

A
f (x) = negative sine (X) minus 1
Option A
B
f (x) = negative 2 sine (x) minus 1
Option B
C
f (x) = negative cosine (x)
Option C
D
f (x) = negative 2 cosine (x) minus 1
Option D
12

Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?

A
155°
B
160°
C
165°
D
170°
13

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
92 = y2 + 192 – 2(y)(19)cos(41°)
B
y2 = 92 + 192 – 2(y)(19)cos(41°)
C
92 = y2 + 192 – 2(9)(19)cos(41°)
D
y2 = 92 + 192 – 2(9)(19)cos(41°)
14

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
34°
B
41°
C
51°
D
56°
15

Heron’s formula: Area =

Question illustration
A
27 square units
B
38 square units
C
364 square units
D
728 square units
16

What is the period of the function ?

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
17

Law of sines:

Question illustration
A
only 90°
B
only 155°
C
20° and 110°
D
45° and 135°
18

Haruto simplified the value below.Which statement explains whether Haruto is correct?

Question illustration
A
Haruto is correct because the angle is coterminal with and the reference angle is .
Option A
B
Haruto is correct because the angle is coterminal with , which is also the reference angle.
Option B
C
Haruto is not correct because the angle is coterminal with , and .
Option C
D
Haruto is not correct because the angle is coterminal with , and .
Option D
19

If , which equation represents ?

Question illustration
A
cotangent theta = StartFraction StartRoot 15 EndRoot Over 8 EndFraction
Option A
B
cotangent theta = StartFraction StartRoot 15 EndRoot Over 7 EndFraction
Option B
C
cotangent theta = StartFraction 7 StartRoot 15 EndRoot Over 15 EndFraction
Option C
D
cotangent theta = StartFraction 8 StartRoot 15 EndRoot Over 15 EndFraction
Option D
20

Which function describes the graph below?

Question illustration
A
f (x) = 6 cosine (x)
Option A
B
f (x) = 3 cosine (x) + 3
Option B
C
f (x) = 6 sine (x)
Option C
D
f (x) = 3 sine (x) + 3
Option D

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