How do you add all of parts (Midline, Amplitude, Period) to create the Final/ full equation?

You need one more piece of information before you can do that: which trig function is being used (sin,cos,etc..) Then you can create the equation. The base equation is just y = sin(x) The full equation looks like: y = A * sin(x * (2pi / B)) + C, Where A is the Amplitude, B is the Period, and C is the Midline. The reason the period is 2pi / B is because the base function's period is 2 pi. Hope this helped!

How to find tan or cot period?

Same method as sin or cos except substitute pi for 2pi. While Period of sin(Cx) = 2pi/C Period of tan(Cx) = pi/C Period of cot(Cx) = pi/C Period of tan() and cot() occurs twice as frequently as sin() cos() because tan() is slope and when you travel halfway (pi radians) around the unit circle, you encounter another point on the same line (same slope).

How do you find out the midline from just the equation (without the graph)?

For f(x)=asin(bx+c)+d, d is the midline. Simple as that.

How do I find the equation of a sinusoidal wave given the frequency and amplitude of the wave?

Awesome question! To write a sine function you simply need to use the following equation: f(x) = asin(bx + c) + d, where a is the amplitude, b is the period (you can find the period by dividing the absolute value b by 2pi; in your case, I believe the frequency and period are the same), c is the phase shift (or the shift along the x-axis), and d is the vertical shift (this value also represents the midline of the function). You can determine the vertical shift by dividing the maximum value plus the minimum value of the graph by 2. The period can be determined using the 2pi/|b| expression,but you might not always have to write it that way in the equation; I'm not quite sure how you would determine the phase shift given only the amplitude and frequency of the wave, but if you could graph the equation of the parent function and the function you have thus far, you might be able to determine the phase shift from that. Doing that will get you a solid equation. I hope this helps!

what if it's a polynomial?

that manipulated equation will help understand the graph

how do you find the value of b in the equation?

b represents the "y-intercept" which is the y-value of the function when it it touches the y-axis (in other words, when it has a x-value of zero). For example, the graph given as an example has a y-intercept of 5 as the graph touches the y-axis when its y value is 5.

after determining the amplitude and period of a function, how do you determine the Sine/Cosine formulae for them in a way that avoids the need to include a phase shift?

I would say most of the time a phase shift is unavoidable. I think the simplest way is to just use what the proble tells you. if it describes the midline I would use sine and if it gives a max or min cosine. If it gives both use whichever comes first. That is with word problems anyway, if you are given a picture then it's a little easier. If there is a point on the midline or a max or min that touches the y axis, then you use sine for a midline point and cosine for a max or min. In these cases then there will not be a phase shift. If there is no nice point that touches the y axis then there is definitely a phase shift. the easiest is to probably pick the closest "nice" point to the y axis then. Does this make sense?

How do you find the midline when you are only given one point (min or max) and the aplidtude?

The amplitude is the vertical distance from the midline to the min or max. So if you are given the minimum, add the amplitude to the y-coordinate. If you are given the maximum, subtract the amplitude from the y-coordinate.

I always seem to have a problem with finding the periodic function.. I just need more help with understanding what is plugged in as "K" in the formula 2pi/K? y=1/2*tan theta-3

The absolute value of the number multiplying the variable (next to the x) in cos(x) or sin(x).

Main content

Integrated math 3

Course: Integrated math 3 > Unit 8

Lesson 9: Amplitude, midline, & period

Midline, amplitude, and period review

Google Classroom

Review the basic features of sinusoidal functions: midline, amplitude, and period.

What are midline, amplitude, and period?

Midline, amplitude, and period are three features of sinusoidal graphs.

Midline

is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.

Amplitude

is the vertical distance between the midline and one of the extremum points.

Period

is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).

Want to learn more about midline, amplitude, and period? Check out this video.

Finding features from graph

Given the graph of a sinusoidal function, we can analyze it to find the midline, amplitude, and period. Consider, for example, the following graph.

It has a maximum point at

(1, 7)

, then a minimum point at

(3, 3)

, then another maximum point at

(5, 7)

The horizontal line that passes exactly between

y = 7

(the maximum value) and

y = 3

(the minimum value) is

y = 5

, so that's the midline.

The vertical distance between the midline and any of the extremum points is

2

, so that's the amplitude.

The distance between the two consecutive maximum points is

4

, so that's the period.

Problem 1

What is the midline equation?

y =

Want to try more problems like this? Check out these exercises:

Midline of sinusoidal functions from graph
Amplitude of sinusoidal functions from graph
Period of sinusoidal functions from graph

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zuhaibindustries
Posted 7 years ago. Direct link to zuhaibindustries's post “How to find tan or cot pe...”
How to find tan or cot period?
Button navigates to signup pageComment on zuhaibindustries's post “How to find tan or cot pe...”
(27 votes)
Answer
- Brent Carter
  Posted 7 years ago. Direct link to Brent Carter's post “Same method as sin or cos...”
  Same method as sin or cos except substitute pi for 2pi.
  
  While Period of sin(Cx) = 2pi/C
  
  Period of tan(Cx) = pi/C
  Period of cot(Cx) = pi/C
  
  Period of tan() and cot() occurs twice as frequently as sin() cos() because tan() is slope and when you travel halfway (pi radians) around the unit circle, you encounter another point on the same line (same slope).
  Button navigates to signup page
  (64 votes)
Sarah Shen
Posted 5 years ago. Direct link to Sarah Shen's post “How do you find out the m...”
How do you find out the midline from just the equation (without the graph)?
Button navigates to signup pageButton navigates to signup page
(14 votes)
Answer
- Madd Sam
  Posted 5 years ago. Direct link to Madd Sam's post “For f(x)=asin(bx+c)+d, d ...”
  For f(x)=asin(bx+c)+d, d is the midline. Simple as that.
  Button navigates to signup page
  (47 votes)
Jaedan
Posted 6 years ago. Direct link to Jaedan's post “How do you add all of par...”
How do you add all of parts (Midline, Amplitude, Period) to create the Final/ full equation?
Button navigates to signup pageComment on Jaedan's post “How do you add all of par...”
(28 votes)
Answer
- masterYoda
  Posted 8 months ago. Direct link to masterYoda's post “You need one more piece o...”
  You need one more piece of information before you can do that: which trig function is being used (sin,cos,etc..)
  Then you can create the equation.
  
  The base equation is just y = sin(x)
  The full equation looks like: y = A * sin(x * (2pi / B)) + C,
  Where A is the Amplitude, B is the Period, and C is the Midline.
  
  The reason the period is 2pi / B is because the base function's period is 2 pi.
  
  Hope this helped!
  Button navigates to signup page
  (2 votes)
Kenneth Wells
Posted 5 years ago. Direct link to Kenneth Wells's post “How do I find the equatio...”
How do I find the equation of a sinusoidal wave given the frequency and amplitude of the wave?
Button navigates to signup pageComment on Kenneth Wells's post “How do I find the equatio...”
(12 votes)
Answer
- Hypernova Solaris
  Posted 5 years ago. Direct link to Hypernova Solaris's post “Awesome question! To wri...”
  Awesome question! To write a sine function you simply need to use the following equation: f(x) = asin(bx + c) + d, where a is the amplitude, b is the period (you can find the period by dividing the absolute value b by 2pi; in your case, I believe the frequency and period are the same), c is the phase shift (or the shift along the x-axis), and d is the vertical shift (this value also represents the midline of the function). You can determine the vertical shift by dividing the maximum value plus the minimum value of the graph by 2. The period can be determined using the 2pi/|b| expression,but you might not always have to write it that way in the equation; I'm not quite sure how you would determine the phase shift given only the amplitude and frequency of the wave, but if you could graph the equation of the parent function and the function you have thus far, you might be able to determine the phase shift from that. Doing that will get you a solid equation. I hope this helps!
  Button navigates to signup page
  (36 votes)
bruh brisa
Posted 8 months ago. Direct link to bruh brisa's post “hey guys”
hey guys
Button navigates to signup pageComment on bruh brisa's post “hey guys”
(12 votes)
Answer
- alansijo
  Posted 7 months ago. Direct link to alansijo's post “hello there”
  hello there
  Comment on alansijo's post “hello there”
  (13 votes)
salmaf1
Posted 4 years ago. Direct link to salmaf1's post “How do you find the midli...”
How do you find the midline when you are only given one point (min or max) and the aplidtude?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- obiwan kenobi
  Posted 4 years ago. Direct link to obiwan kenobi's post “The amplitude is the vert...”
  The amplitude is the vertical distance from the midline to the min or max. So if you are given the minimum, add the amplitude to the y-coordinate. If you are given the maximum, subtract the amplitude from the y-coordinate.
  Button navigates to signup page
  (17 votes)
C Jacob Brennan
Posted 7 years ago. Direct link to C Jacob Brennan's post “what if it's a polynomial...”
what if it's a polynomial?
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(7 votes)
Answer
- Melissa Megias
  Posted 6 years ago. Direct link to Melissa Megias's post “that manipulated equation...”
  that manipulated equation will help understand the graph
  Button navigates to signup page
  (4 votes)
430901
Posted 4 years ago. Direct link to 430901's post “how do you find the value...”
how do you find the value of b in the equation?
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(6 votes)
Answer
- Bradley Reynolds
  Posted 4 years ago. Direct link to Bradley Reynolds's post “b represents the "y-inter...”
  b represents the "y-intercept" which is the y-value of the function when it it touches the y-axis (in other words, when it has a x-value of zero). For example, the graph given as an example has a y-intercept of 5 as the graph touches the y-axis when its y value is 5.
  Comment on Bradley Reynolds's post “b represents the "y-inter...”
  (6 votes)
sophspellissy
Posted 3 years ago. Direct link to sophspellissy's post “after determining the amp...”
after determining the amplitude and period of a function, how do you determine the Sine/Cosine formulae
for them in a way that avoids the need to include a phase shift?
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- loumast17
  Posted 3 years ago. Direct link to loumast17's post “I would say most of the t...”
  I would say most of the time a phase shift is unavoidable. I think the simplest way is to just use what the proble tells you. if it describes the midline I would use sine and if it gives a max or min cosine. If it gives both use whichever comes first.
  
  That is with word problems anyway, if you are given a picture then it's a little easier. If there is a point on the midline or a max or min that touches the y axis, then you use sine for a midline point and cosine for a max or min. In these cases then there will not be a phase shift. If there is no nice point that touches the y axis then there is definitely a phase shift. the easiest is to probably pick the closest "nice" point to the y axis then.
  
  Does this make sense?
  Button navigates to signup page
  (5 votes)
Briaalexander17
Posted 7 years ago. Direct link to Briaalexander17's post “I always seem to have a p...”
I always seem to have a problem with finding the periodic function.. I just need more help with understanding what is plugged in as "K" in the formula 2pi/K?
y=1/2*tan theta-3
Button navigates to signup pageComment on Briaalexander17's post “I always seem to have a p...”
(5 votes)
Answer
- DoctorD.CollegeDoc
  Posted 7 years ago. Direct link to DoctorD.CollegeDoc's post “The absolute value of the...”
  The absolute value of the number multiplying the variable (next to the x) in cos(x) or sin(x).
  Button navigates to signup page
  (5 votes)