AnswersPre Calculus AGeneral Form of Sine and Cosine

General Form of Sine and Cosine Answers

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1
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An object travels back and forth along a straight line. Its velocity, in centimeters per second, is given by the function v(t) = , where t is time in seconds.What is the maximum velocity of the object?

Question illustration
A
0 cm/s
B
13 cm/s
C
26 cm/s
D
90 cm/s
2
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Which graph represents the function ?

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A
On a coordinate plane, a function has a maximum of 1 and minimum of negative 1. It completes one period at 2 pi. It crosses the y-axis at (0, 1).
Option A
B
On a coordinate plane, a function has a maximum of 0 and minimum of negative 2. It completes one period at 2 pi. It crosses the y-axis at (0, 0).
Option B
C
On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, 1).
Option C
D
On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, negative 3).
Option D
3

Review the given functions.

Question illustration
A
a shift left units
Option A
B
a shift left units
Option B
C
a shift right units
Option C
D
a shift right units
Option D
4

The blades of a wind turbine are 135 feet long and are attached to the top of a 262-foot tower. The turbine completes 17 revolutions per minute. Suppose the tip of one of the blades starts at its maximum height above the ground.Which function represents the height, in feet, of the tip of this blade after t minutes?

A
f (t) = 270 cosine (17 pi t) + 262
Option A
B
f (t) = 135 cosine (17 pi t) + 262
Option B
C
f (t) = 270 cosine (34 pi t) + 262
Option C
D
f (t) = 135 cosine (34 pi t) + 262
Option D
5

A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = , where x is time in minutes.How many times does the fan rotate each minute?

Question illustration
A
1,000
B
2,000
C
4,000
D
6,000
6

Which graph represents the function g(x) = 7cosx after a shift of units to the right?

Question illustration
A
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, 6).
Option A
B
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It decreases through the y-axis at (0, 4).
Option B
C
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, negative 6).
Option C
D
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It increases through the y-axis at (0, 4).
Option D
7

Suppose the function f(t) = models the height of a seat on a Ferris wheel after t minutes.Based on this information, what is the diameter of the Ferris wheel?

Question illustration
A
95 ft
B
120 ft
C
190 ft
D
215 ft
8

The graph displays the function g(x) .

Question illustration
A
h (x) = 2 cosine (x minus StartFraction 3 pi Over 8 EndFraction) minus 1
Option A
B
h (x) = 2 cosine (x minus StartFraction 3 pi Over 8 EndFraction) minus 3
Option B
C
h (x) = 2 cosine (x + StartFraction 11 pi Over 8 EndFraction) minus 1
Option C
D
h (x) = 2 cosine (x + StartFraction 11 pi Over 8 EndFraction) minus 3
Option D
9

The water depth in a harbor rises and falls over time. The function f(t) = models the water depth, in feet, after t hours.During the first 24 hours, at what times does the water depth reach a maximum?

Question illustration
A
at 5 and 17 hours
B
at 11 and 23 hours
C
at 2, 8, 14, and 20 hours
D
at 5, 11, 17, and 23 hours
10

The position of a paddle on a waterwheel after t seconds is modeled by f(t) = . A positive function value indicates the paddle is above the waterline, while a negative value indicates the paddle is below the waterline.What is the initial position of the paddle?

Question illustration
A
10.5 ft above the waterline
B
5.25 ft above the waterline
C
0 ft at the waterline
D
5.25 ft below the waterline

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