Sinusoidal Modeling Quiz

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Quizzes Created: 1110 | Total Attempts: 2,473,266

Questions: 10 | Attempts: 159 | Updated: Aug 16, 2023

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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.

Questions and Answers

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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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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