Question 1

State the period of the function.

Accepted Answer

The answer of State the period of the function. 
...

Question 2

Graph the function by using translations.

Accepted Answer

The answer of Graph the function by using translations. 
...

Question 3

State the period of the function.

Accepted Answer

The answer of State the period of the function. 
...

Question 4

Write an equation for the simple harmonic motion that satisfies the given conditions. Assume that the maximum displacement occurs at t = 0. Frequency = 1.2 cycles per second, amplitude = 5 centimeters

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The answer of Write an equation for the simple harmonic...

Question 5

Graph the function.

Accepted Answer

The answer of Graph the function. 
...

Question 6

Find the amplitude, phase shift, and period for the graph of the function.

Accepted Answer

The answer of Find the amplitude, phase shift, and period...

Question 7

State the amplitude and period of the function defined by the equation.

Accepted Answer

Amplitude is the distance from the peak (or trough) of the wave to the middle line. Looking at the graph of the function, we can see that the amplitude is 2.

Period is the length of one complete cycle of the wave. From the graph, we can see that the length of one complete cycle is 1.5 units. Therefore, the period is 1.5π.

Choice C has an amplitude of 2 and a period of 1.5π, which matches our calculations.

Question 8

Find the amplitude, period, and frequency of the simple harmonic motion.

Accepted Answer

The answer of Find the amplitude, period, and frequency of...

Question 9

Graph the given function by using the addition-of-ordinates method.

Accepted Answer

The answer of Graph the given function by using the...

Question 10

Assume that a mass of m pounds on the end of a spring is oscillating in simple harmonic motion. What will be the effect on the period of the motion if the mass is increased to 25 m ?

Accepted Answer

The period of a mass-spring system is given by T=2π√(m/k), where m is the mass and k is the spring constant. If the mass is increased to 25m, then the period becomes T=2π√(25m/k)=2π(5)√(m/k). This means the period has increased by a factor of 5, so the new period is 5 times the original period. Therefore, the correct choice is D.

Question 11

State the values for which the function is undefined.

Accepted Answer

The answer of State the values for which the function...

Question 12

Find the amplitude, period, and frequency of the simple harmonic motion.

Accepted Answer

The answer of Find the amplitude, period, and frequency of...

Question 13

Use the information below to find cos t given  .

Accepted Answer

The answer of Use the information below to find cos...

Question 14

Find the phase shift and the period for the graph of the function.

Accepted Answer

The given function is not specified, so we cannot determine the phase shift and period directly from the graph. However, we can see that the curve has exactly one peak and one trough within one complete cycle. This implies that the graph is of a cosine function, which has a period of 2π. Therefore, the period of the given function is also 2π. 
To find the phase shift, we need to look for the horizontal shift of the graph. Since the curve has one peak and one trough within one complete cycle, we can assume that the horizontal axis intercepts the graph at one of these points. For cosine functions, the curve intersects the x-axis at a peak when the phase shift is 0, and at a trough when the phase shift is π. Therefore, the phase shift is either 0 or π. 
We can estimate the horizontal shift by comparing the given graph with the standard cosine function y = cos(x). The graph is shifted to the right if it reaches its maximum after the standard cosine function, and shifted to the left if it reaches its maximum before the standard cosine function. By comparing the given graph with y = cos(x), we can see that the maximum of the given function occurs at x = π/2, which is to the right of the maximum of y = cos(x) at x = 0. This means that the graph of the given function is shifted to the right by π/2, which gives a phase shift of π/2. Therefore, we choose answer choice B, which gives the correct phase shift and period.

Question 15

Graph the function defined by the equation.

Accepted Answer

The answer of Graph the function defined by the equation....

Question 16

Graph the function defined by the equation.

Accepted Answer

The given equation is not provided in the question. Therefore, it is impossible to determine which graph is the correct one without the equation.

Question 17

Graph the function defined by the equation.

Accepted Answer

The answer of Graph the function defined by the equation....

Question 18

Write an equation for the simple harmonic motion that satisfies the given conditions. Assume that the maximum displacement occurs when t = 0. Amplitude = 3.5 inches, frequency 1.5 cycles per second

Accepted Answer

The answer of Write an equation for the simple harmonic...

Quiz 5: Trigonometric Functions

State the period of the function.

Graph the function by using translations.

State the period of the function.

Write an equation for the simple harmonic motion that satisfies the given conditions. Assume that the maximum displacement occurs at t = 0. Frequency = 1.2 cycles per second, amplitude = 5 centimeters

Graph the function.

Find the amplitude, phase shift, and period for the graph of the function.

State the amplitude and period of the function defined by the equation.

Find the amplitude, period, and frequency of the simple harmonic motion.

Graph the given function by using the addition-of-ordinates method.

Assume that a mass of m pounds on the end of a spring is oscillating in simple harmonic motion. What will be the effect on the period of the motion if the mass is increased to 25 m ?

State the values for which the function is undefined.

Find the amplitude, period, and frequency of the simple harmonic motion.

Use the information below to find cos t given .

Find the phase shift and the period for the graph of the function.

Graph the function defined by the equation.

Graph the function defined by the equation.

Graph the function defined by the equation.

Write an equation for the simple harmonic motion that satisfies the given conditions. Assume that the maximum displacement occurs when t = 0. Amplitude = 3.5 inches, frequency 1.5 cycles per second