Question 1

Select the graph of the function.(Include two full periods.) ​  ​

Accepted Answer

This graph represents a sine function with an amplitude of 3 and a period of 4. The graph has four points where it intersects the x-axis, which corresponds to four full periods. Choice C is the only graph that fits these criteria.

Question 2

Use a graphing utility to select the graph of the function.Include two full periods.  ​

Accepted Answer

The answer of Use a graphing utility to select the...

Question 3

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of 4π, an amplitude of 4, a left phase shift of  , and a vertical translation down 5 units.
​

Accepted Answer

The general equation for a sine curve with amplitude A, period B, left phase shift C, and vertical translation D is:

y = A*sin((2*pi/B)*(x-C))+D

Plugging in the given values, we get:

y = 4*sin((2*pi/(4*pi))*(x-11))+(-5)

Simplifying:

y = 4*sin(0.5*(x-11))-5

This matches the equation given in choice C.

Question 4

Select the graph of the function.(Include two full periods.) ​  ​

Accepted Answer

The graph in choice B shows a periodic function with a maximum value of approximately 3 at x = -1 and x = 5, and a minimum value of approximately -3 at x = -3 and x = 3. The function appears to repeat every 4 units of x, indicating a period of 4. The graph also shows a symmetric, sinusoidal shape, indicating a trigonometric function. None of the other graphs display these characteristics.

Question 5

Use a graphing utility to select the graph of the function.Include two full periods. ​
Y = -2 sin (2x + π)
​

Accepted Answer

The graph in choice B shows two full periods of the function Y = -2 sin (2x + π). It also correctly reflects the amplitude (-2) and period (π).

Question 6

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​
Y = 0.001 sin 880πt,
​
Where t is the time (in seconds).
​
What is the period of the function?
​

Accepted Answer

The period of a sinusoidal function is the amount of time it takes for one complete cycle. In this case, the function is Y = 0.001 sin 880πt, which represents one complete cycle of a sound wave with a frequency of 880 Hz (the A note above middle C). The equation for the period of a sinusoidal function is T = 2π/ω, where ω is the angular frequency (in radians per second). In this case, ω = 880π, so T = 2π/880π = 1/440 seconds. Converted to scientific notation, this is 2.27 x 10^-3 seconds, which is equivalent to 11.3 milliseconds. Therefore, the period of the function is approximately 11.3 milliseconds, or 1.13 x 10^-2 seconds. The closest answer choice is C, which is 11eacce6_1d5e_ae12_9f49_67599fbfd178_TB7896_11 sec.

Question 7

Select the graph of the function.(Include two full periods.) ​  ​

Accepted Answer

The answer of Select the graph of the function.(Include two...

Question 8

Select the graph of the function.(Include two full periods.) ​  ​

Accepted Answer

The graph has a sine-like shape with an amplitude of 2 and a period of 4pi/3. Choice B shows two full periods of such a function.

Question 9

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​  ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
​
Find the number of cycles per minute.
​

Accepted Answer

The answer of After exercising for a few minutes, a...

Question 10

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by ​  ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
​
Find the number of cycles per minute.
​

Accepted Answer

The answer of For a person at rest, the velocity...

Question 11

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​
Y = 0.001 sin 850πt,
​
Where t is the time (in seconds).
​
The frequency is given by f = 1 / p.What is the frequency of the note?
​

Accepted Answer

The answer of When tuning a piano, a technician strikes...

Question 12

Select the graph of the function.(Include two full periods.) ​  ​

Accepted Answer

The answer of Select the graph of the function.(Include two...

Question 13

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by ​  ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0, and exhalation occurs when v < 0.)
​
Find the time for one full respiratory cycle.
​

Accepted Answer

The answer of For a person at rest, the velocity...

Question 14

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​  ,
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
​
Find the time for one full respiratory cycle.​
​

Accepted Answer

The answer of After exercising for a few minutes, a...

Question 15

Write an equation for the function that is described by the given characteristics. ​
A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of  , and a vertical translation up 2 units.
​

Accepted Answer

The answer of Write an equation for the function that...

Question 16

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​  ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
Select the graph of this velocity function.

Accepted Answer

The answer of After exercising for a few minutes, a...

Question 17

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by ​  ,
​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
Select the graph of this velocity function.
​

Accepted Answer

The graph should have a period of approximately 5 seconds and alternate between positive and negative values, representing inhalation and exhalation, respectively. The graph in choice A satisfies these requirements, while the others do not. Choice B has a period of approximately 3 seconds and does not have alternating positive and negative values. Choices C, D, and E have periods that are too large and do not have alternating positive and negative values.

Question 18

Write an equation for the function that is described by the given characteristics. ​
A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down  units.
​

Accepted Answer

The answer of Write an equation for the function that...

Question 19

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of π, an amplitude of 4, a right phase shift of  , and a vertical translation up 7 units.
​

Accepted Answer

The answer of Write an equation for the function that...

Question 20

Use a graphing utility to select the graph of the function.Include two full periods. ​  ​

Accepted Answer

The answer of Use a graphing utility to select the...

Quiz 1: Trigonometry

Select the graph of the function.(Include two full periods.)

Use a graphing utility to select the graph of the function.Include two full periods.

Write an equation for the function that is described by the given characteristics. A sine curve with a period of 4π, an amplitude of 4, a left phase shift of , and a vertical translation down 5 units.

Select the graph of the function.(Include two full periods.)

Use a graphing utility to select the graph of the function.Include two full periods. Y = -2 sin (2x + π)

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by Y = 0.001 sin 880πt, Where t is the time (in seconds) . What is the period of the function?

Select the graph of the function.(Include two full periods.)

Select the graph of the function.(Include two full periods.)

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Find the number of cycles per minute.

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by Y = 0.001 sin 850πt, Where t is the time (in seconds) . The frequency is given by f = 1 / p.What is the frequency of the note?

Select the graph of the function.(Include two full periods.)

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Find the time for one full respiratory cycle.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of , and a vertical translation up 2 units.

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units.

Write an equation for the function that is described by the given characteristics. A sine curve with a period of π, an amplitude of 4, a right phase shift of , and a vertical translation up 7 units.

Use a graphing utility to select the graph of the function.Include two full periods.

Quiz 1: Trigonometry

Select the graph of the function.(Include two full periods.) ​ ​

Use a graphing utility to select the graph of the function.Include two full periods. ​

Write an equation for the function that is described by the given characteristics. ​ A sine curve with a period of 4π, an amplitude of 4, a left phase shift of , and a vertical translation down 5 units. ​

Select the graph of the function.(Include two full periods.) ​ ​

Use a graphing utility to select the graph of the function.Include two full periods. ​ Y = -2 sin (2x + π) ​

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​ Y = 0.001 sin 880πt, ​ Where t is the time (in seconds) . ​ What is the period of the function? ​

Select the graph of the function.(Include two full periods.) ​ ​

Select the graph of the function.(Include two full periods.) ​ ​

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​ , ​ Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) ​ Find the number of cycles per minute. ​

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​ Y = 0.001 sin 850πt, ​ Where t is the time (in seconds) . ​ The frequency is given by f = 1 / p.What is the frequency of the note? ​

Select the graph of the function.(Include two full periods.) ​ ​

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​ , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) ​ Find the time for one full respiratory cycle.​ ​

Write an equation for the function that is described by the given characteristics. ​ A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of , and a vertical translation up 2 units. ​

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by ​ , ​ Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function.

Write an equation for the function that is described by the given characteristics. ​ A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units. ​

Write an equation for the function that is described by the given characteristics. ​ A sine curve with a period of π, an amplitude of 4, a right phase shift of , and a vertical translation up 7 units. ​

Use a graphing utility to select the graph of the function.Include two full periods. ​ ​

Select the graph of the function.(Include two full periods.)

Use a graphing utility to select the graph of the function.Include two full periods.

Write an equation for the function that is described by the given characteristics. A sine curve with a period of 4π, an amplitude of 4, a left phase shift of , and a vertical translation down 5 units.

Select the graph of the function.(Include two full periods.)

Use a graphing utility to select the graph of the function.Include two full periods. Y = -2 sin (2x + π)

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by Y = 0.001 sin 880πt, Where t is the time (in seconds) . What is the period of the function?

Select the graph of the function.(Include two full periods.)

Select the graph of the function.(Include two full periods.)

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Find the number of cycles per minute.

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by Y = 0.001 sin 850πt, Where t is the time (in seconds) . The frequency is given by f = 1 / p.What is the frequency of the note?

Select the graph of the function.(Include two full periods.)

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Find the time for one full respiratory cycle.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of 4π, an amplitude of 7, a right phase shift of , and a vertical translation up 2 units.

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by , Where t is the time (in seconds) . (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units.

Write an equation for the function that is described by the given characteristics. A sine curve with a period of π, an amplitude of 4, a right phase shift of , and a vertical translation up 7 units.

Use a graphing utility to select the graph of the function.Include two full periods.