Determining Sin wave horizontal shift 'C' value

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To determine the sine wave's horizontal shift 'C' value, the equation format y=a*sin[b*(x-c)] + d is used. The amplitude 'a' is calculated as 5, the frequency 'b' is found to be 2, and the vertical shift 'd' is 3. The challenge lies in correctly identifying 'c', with the first maximum occurring at (pi/5, 8) and the reference maximum at pi/2. The correct approach involves setting the argument of the sine function equal to pi/2 and solving for 'c', leading to the conclusion that 'c' should be pi/20.
tsaitea
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Find the equation of a sine function with its first positive maximum point at (pi/5,8) and its next minimum point at (7pi/10,-2).

With the sin form as y=a*sin[b*(x-c)] + d

I found:

a=[max-min]/2 = 5
b= 2pi/period= 2pi/(2*[max-min])=2
d=max+min/2=3

I am having troubles determining the value for c.

How I am thinking about is that the point of reference for sin when it hits its first maximum is at pi/2. The difference between the pi/2 and pi/5 would be my phase shift however the answer is not right. The value for c should be pi/20.

Can someone explain what I have done incorrectly here?
 
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tsaitea said:
Find the equation of a sine function with its first positive maximum point at (pi/5,8) and its next minimum point at (7pi/10,-2).

With the sin form as y=a*sin[b*(x-c)] + d

I found:

a=[max-min]/2 = 5
b= 2pi/period= 2pi/(2*[max-min])=2
d=max+min/2=3

I am having troubles determining the value for c.

How I am thinking about is that the point of reference for sin when it hits its first maximum is at pi/2. The difference between the pi/2 and pi/5 would be my phase shift however the answer is not right. The value for c should be pi/20.

Can someone explain what I have done incorrectly here?
sin(x) has its first max at x = π/2 -- basically when its argument is π/2 .

What is the argument of the sine function appearing in your expression?
 
My argument is 2(x+3pi/10)
 
tsaitea said:
My argument is 2(x+3pi/10)
So, you've found c ?
 
Yes, but the correct answer for the argument is 2(x+pi/20)
 
Ahh I think I got it... so what I am supposed to do is set the argument at pi/5 equal to pi/2 and solve for c like this...

2(pi/5 -c) = pi/2

Thanks for your help!
 
tsaitea said:
My argument is 2(x+3pi/10)

So the argument is 2(x - c) .

That should equal π/2 at the first maximum. Right?

You know the x value at the first max., so plug that in & solve.
 

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