When you think of a trigonometric function of the form y = A s i n ( B x + C ) + D, the amplitude is represented by A, or the coefficient in front of the sine function. While this number is -24, we always represent amplitude as a positive number, by taking the absolute value of it. Therefore, the amplitude of this function is 24.
Select the answer choice that correctly matches each function to its period.
Possible Answers: Correct answer: Explanation :The following matches the correct period with its corresponding trig function:
In other words, sin x, cos x, sec x, and csc x all repeat themselves every units. However, tan x and cot x repeat themselves more frequently, every units.
What is the period of this sine graph?
The graph has 3 waves between 0 and , meaning that the length of each of the waves is divided by 3, or .
Write the equation for a cosine graph with a maximum at and a minimum at .
Possible Answers: Correct answer: Explanation :In order to write this equation, it is helpful to sketch a graph:
The dotted line is at , where the maximum occurs and therefore where the graph starts. This means that the graph is shifted to the right .
The distance from the maximum to the minimum is half the entire wavelength. Here it is .
Since half the wavelength is , that means the full wavelength is so the frequency is just 1.
The amplitude is 3 because the graph goes symmetrically from -3 to 3.
The equation will be in the form where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift.
This equation is
Find the phase shift of .
Possible Answers: Correct answer: Explanation :represents the phase shift.
Plugging in what we know gives us:
Simplified, the phase is then .
Which equation would produce this sine graph?
The graph has an amplitude of 2 but has been shifted down 1:
In terms of the equation, this puts a 2 in front of sin, and -1 at the end.
This makes it easier to see that the graph starts [is at 0] where .
The phase shift is to the right, or .
Which of the following equations could represent a cosine function with amplitude 3, period , and a phase shift of ?
Possible Answers: Correct answer: Explanation :The form of the equation will be
First, think about all possible values of A that could give you an amplitude of 3. Either A = -3 or A = 3 could each produce amplitude = 3. Be sure to look for answer choices that satisfy either of these.
Secondly, we know that the period is . Normally we know what B is and need to find the period, but this is the other way around. We can still use the same equation and solve:
. You can cross multiply to solve and get B = 4.
Finally, we need to find a value of C that satisfies
. Cross multiply to get:
Next, plug in B= 4 to solve for C:
Putting this all together, the equation could either be:
State the amplitude, period, phase shift, and vertical shift of the function
Possible Answers:Vertical Shift: -4
Vertical Shift: -4
Vertical Shift: -4
Vertical Shift: 4
Correct answer:Vertical Shift: -4
Explanation :A common way to make sense of all of the transformations that can happen to a trigonometric function is the following. For the equations y = A sin(Bx + C) + D,
In our equation, A=-7, B=6, C=, and D=-4. Next, apply the above numbers to find amplitude, period, phase shift, and vertical shift.
To find amplitude, look at the coefficient in front of the sine function. A=-7, so our amplitude is equal to 7.
The period is 2/B, and in this case B=6. Therefore the period of this function is equal to 2/6 or /3.
To find the phase shift, take -C/B, or -/6. Another way to find this same value is to set the inside of the parenthesis equal to 0, then solve for x.
6x+=0
6x=-
x=-/6
Either way, our phase shift is equal to -/6.
The vertical shift is equal to D, which is -4.
State the amplitude, period, phase shift, and vertical shift of the function
Possible Answers:Vertical Shift: 0
Vertical Shift: 3
Vertical Shift: 3
Vertical Shift: 3
Vertical Shift: 3
Correct answer:Vertical Shift: 3
Explanation :A common way to make sense of all of the transformations that can happen to a trigonometric function is the following. For the equations y = A sin(Bx + C) + D,
In our equation, A=-1, B=1, C=-, and D=3. Next, apply the above numbers to find amplitude, period, phase shift, and vertical shift.
To find amplitude, look at the coefficient in front of the sine function. A=-1, so our amplitude is equal to 1.
The period is 2/B, and in this case B=1. Therefore the period of this function is equal to 2.
To find the phase shift, take -C/B, or . Another way to find this same value is to set the inside of the parenthesis equal to 0, then solve for x.
x-=0
x=
Either way, our phase shift is equal to .
The vertical shift is equal to D, which is 3.
State the amplitude, period, phase shift, and vertical shift of the function
Possible Answers:Vertical Shift: 2
Vertical Shift: -2
Vertical Shift: 2
Vertical Shift: 2
Correct answer:Vertical Shift: 2
Explanation :A common way to make sense of all of the transformations that can happen to a trigonometric function is the following. For the equations y = A sin(Bx + C) + D,
In our equation, A=1, B=2, C=-3, and D=2. Next, apply the above numbers to find amplitude, period, phase shift, and vertical shift.
To find amplitude, look at the coefficient in front of the sine function. A=1, so our amplitude is equal to 1.
The period is 2/B, and in this case B=2. Therefore the period of this function is equal to .
To find the phase shift, take -C/B, or 3/2. Another way to find this same value is to set the inside of the parenthesis equal to 0, then solve for x.
2x-3=0
2x=3
x=3/2
Either way, our phase shift is equal to 3/2.
The vertical shift is equal to D, which is 2.
If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.
If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.
Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.
Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.
Please follow these steps to file a notice:
You must include the following:
A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.
Send your complaint to our designated agent at:
Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105
Or fill out the form below:
