Find a, b and c from the curve (graph) showing three points on y = a + b*sin(cx)

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Kulla_9289

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I have a sine curve as attached and was told to find a, b, and c. The amplitude is 4 and the vertical shift is 2. How do you find the period cycle?
 

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Kulla_9289 said:
I have a sine curve as attached and was told to find a, b, and c. The amplitude is 4 and the vertical shift is 2. How do you find the period cycle?
Click to expand...
You have three easy point on this curve: [imath] (0,2), (\pi, 2), (\pi/2, 6)[/imath]

So put those into y = a + b sin(cx). That will give you three equations in three unknowns.

Give it a try and post what you've got if you need more help.

-Dan
 
How would you solve it? I substituted and got three equations. After substituting into two of the sine equations, I am stuck.
 
Kulla_9289 said:
How would you solve it? I substituted and got three equations. After substituting into two of the sine equations, I am stuck.
Click to expand...
[imath]2 = a + b \, sin(c \cdot 0)[/imath]

What's a?

[imath]2 = a + b \, sin(c \cdot \pi )[/imath]

[imath]6 = a + b \, sin(c \cdot \pi/2)[/imath]

For the sake of argument, let' say that a = 0. (It isn't.)

[imath]2 = b \, sin( \pi c)[/imath]

[imath]6 = b \, sin(\pi c/2)[/imath]

Rewrite the first equation in terms of [imath]sin( 2 (\pi c/2) )[/imath] and use the double angle formula. The second equation gives you the necessary sine term. How do you get the cosine term?

-Dan
 
Kulla_9289 said:
I have a sine curve as attached and was told to find a, b, and c. The amplitude is 4 and the vertical shift is 2. How do you find the period cycle?
Click to expand...
Since you know the vertical shift (and there is no horizontal (phase) shift), you know where the center line of the graph is. Where does it cross that line? Do you see that that is half a cycle?
 
Yes, there are nodes at the endpoints of the given domain. The difference between two nodes on a sinusoid is half a period.
 
Do you mean that, if the difference between to crests is x, then the nodes will be x/2? x/2 = π. So, x = 2π, which is the period.
 
Kulla_9289 said:
Do you mean that, if the difference between to crests is x, then the nodes will be x/2? x/2 = π. So, x = 2π, which is the period.
Click to expand...

Yes. The given graph shows a half period. So the period is 2π. What must c be then?
 
You should be able to solve this system of equations.

2=a+bsin(c⋅0)
c*0=0. sin(0)=0
b*0=0
So bsin(c*0)=0
2=a+bsin(c⋅0)
2=a+0
2=a

Now you try to find b and c.
 
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