# Sinusoidal Modeling Quiz

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What do you know about sinusoidal modeling in math? Are you ready to take this sinusoidal modeling quiz? A sine wave, sinusoidal wave, or you can say just sinusoid, is known as a mathematical curve that is defined in terms of the sine trigonometric function, of which it is the graph. So, we have designed a few questions for your practice. Let's see if you can pass this quiz. All the best to you.

• 1.

### The equation of the graph is

• A.

Y = 3 cos x

• B.

Y = 4 cos x

• C.

Y = 6 cos x

• D.

Y = 5 cos x

D. Y = 5 cos x
Explanation
The correct answer is y = 5 cos x because the equation y = 5 cos x represents a cosine function with an amplitude of 5, which means the graph will oscillate between -5 and 5. The cosine function has a period of 2π, so the graph will repeat itself every 2π units along the x-axis.

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• 2.

### The amplitude of the graph is

• A.

3

• B.

6

• C.

9

• D.

12

A. 3
Explanation
The amplitude of a graph refers to the maximum displacement or distance from the equilibrium position. In this case, the amplitude is given as 3, which means that the graph reaches a maximum displacement of 3 units from the equilibrium position.

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• 3.

### The graph of cosine begins at (0,1).

• A.

True

• B.

False

A. True
Explanation
The graph of cosine begins at (0,1) because at the starting point of the graph, which is at x=0, the value of cosine is 1. As x increases or decreases from 0, the value of cosine changes accordingly, but at x=0, the value is always 1.

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• 4.

### This graph represents ________ trig function.

• A.

Sec

• B.

Sin

• C.

Cos

• D.

None of these

C. Cos
Explanation
The graph represents the cosine (cos) trigonometric function. The cosine function is a periodic function that oscillates between -1 and 1. It represents the x-coordinate of a point on the unit circle as it rotates counterclockwise. The graph of the cosine function starts at its maximum value of 1, then decreases to its minimum value of -1, and repeats this pattern indefinitely. Therefore, the correct answer is "Cos".

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• 5.

### The equation of this graph is x=2cos2x.

• A.

True

• B.

False

B. False
Explanation
The equation x=2cos2x does not represent a graph. It is not possible to have a single equation that represents a graph in this format. Typically, equations that represent graphs involve both x and y variables. Therefore, the statement is false.

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• 6.

### This graph represents ________ trig function.

• A.

Cos

• B.

Sin

• C.

Sec

• D.

None of these

A. Cos
Explanation
This graph represents the cosine (cos) trigonometric function.

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• 7.

### This graph represents ________ trig function.

• A.

Sin

• B.

Cos

• C.

Sec

• D.

None of these

B. Cos
Explanation
This graph represents the cosine (cos) trigonometric function. The cosine function is a periodic function that oscillates between -1 and 1, with a period of 2π. It is used to describe the relationship between the angles and sides of a right triangle. The graph of the cosine function starts at its maximum value of 1, decreases to its minimum value of -1, and then repeats this pattern indefinitely.

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• 8.

### The period of y=4cos5x 2π/5

• A.

True

• B.

False

A. True
Explanation
The given equation is in the form y = A*cos(Bx + C), where A = 4, B = 5, and C = 2π/5. The period of a cosine function is given by 2π/B. Therefore, the period of y = 4cos5x is 2π/5. Since the given equation has an additional term of 2π/5, the period is still 2π/5. Hence, the answer is True.

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• 9.

### The equation of this graph is y=2sin2x.

• A.

True

• B.

False

A. True
Explanation
The equation y=2sin2x represents a sinusoidal function with an amplitude of 2 and a period of π. The coefficient of 2 in front of sin(2x) stretches the graph vertically by a factor of 2. Therefore, the given graph is indeed represented by the equation y=2sin2x.

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• 10.

### This graph represents ________ trig function.

• A.

Sec

• B.

Cos

• C.

Both A & B

• D.

Sin

D. Sin
Explanation
The graph represents the sine trigonometric function. This can be determined by observing the shape of the graph, which exhibits the characteristic wave-like pattern of the sine function. The sine function represents the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.

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• Current Version
• Aug 16, 2023
Quiz Edited by
ProProfs Editorial Team
• Oct 31, 2022
Quiz Created by
Keith Foster

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