AnswersSS26 Math 3 S2 M3960OXGraphing Tangent and Cotangent

Graphing Tangent and Cotangent — Unit test Answers

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

Question illustration
A
72 = 82 + 112 – 2(8)(11)cos(N)
B
82 = 72 + 112 – 2(7)(11)cos(M)
C
72 = 82 + 112 – 2(8)(11)cos(P)
D
82 = 72 + 112 – 2(7)(11)cos(P)
2
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Angle B has a measure between 0° and 360° and is coterminal with a –865° angle. What is the measure of angle B?

A
110°
B
115°
C
210°
D
215°
3

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin?

Question illustration
A
One-fifth
Option A
B
StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
2
Option D
4

Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?

Question illustration
A
The reference angle should be , and the sign of the value should be negative.
Option A
B
The reference angle should be , and the cosine value for is .
Option B
C
The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting in the first step.
Option C
D
The cosine value for is , and the reference angle and quadrant should be determined by subtracting in the first step.
Option D
5

A parallelogram has side lengths of 4 and 6 and an angle of measure 55°.Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
3
B
5
C
6
D
7
6

Which function is the same as ?

Question illustration
A
y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option A
B
y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option B
C
y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option C
D
y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
Option D
7

The law of cosines is used to find the value of m.

Question illustration
A
13
B
14
C
43
D
45
8

Which formula gives the zeros of y = sin(x)?

A
for any positive integer k
Option A
B
for any integer k
Option B
C
for any positive integer k
Option C
D
for any integer k
Option D
9

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.Law of cosines:

Question illustration
A
589 meters
B
705 meters
C
792 meters
D
861 meters
10

The parent cosecant function is shifted 2 units down, and its period is changed to . Which of the following is the graph of the transformed function?

Question illustration
A
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 1 at (3 by 2 pi comma negative 1) and (negative 9 by 2 pi comma negative 1). Another line y equals negative 3 touches at (3 by 2 pi comma negative 3) and (negative 9 by 2 pi comma negative 3).
Option A
B
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (3 by 2 pi comma1) and (negative 9 by 2 pi comma 1). Another line y equals negative 1 touches at (9 by 2 pi comma negative 1) and (negative 3 by 2 pi comma negative 1).
Option B
C
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 3 touches at (3 pi comma negative 3) and (negative 3 pi comma negative 3).
Option C
D
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 2 touches at (3 pi comma negative 1) and (negative 3 pi comma negative 1).
Option D
11

Heron’s formula: Area =

Question illustration
A
square units
Option A
B
square units
Option B
C
square units
Option C
D
square units
Option D
12

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

Question illustration
A
1.9 units
B
4.7 units
C
5.0 units
D
5.7 units
13

What is the general equation of a sine function with an amplitude of 6, a period of , and a horizontal shift of ?

Question illustration
A
y = sine (8 (x minus StartFraction pi Over 2 EndFraction))
Option A
B
y = 8 sine (4 (x minus StartFraction pi Over 2 EndFraction))
Option B
C
y = 6 sine (8 (x minus StartFraction pi Over 2 EndFraction))
Option C
D
y = 6 sine (8 x) + StartFraction pi Over 2 EndFraction
Option D
14

Which transformations are needed to change the parent sine function to the sine function below?

Question illustration
A
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left
Option A
B
vertical stretch of 2, horizontal compression to a period of , vertical shift of 2 units up, phase shift of units left
Option B
C
vertical stretch of , horizontal compression to a period of , vertical shift of 1 unit up, phase shift of units left
Option C
D
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit down, phase shift of units left
Option D
15

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option D

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