Determining Sin wave horizontal shift 'C' value

[tsaitea]

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?

 

[SammyS]

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?

 

[tsaitea]

My argument is 2(x+3pi/10)

 

[SammyS]

My argument is 2(x+3pi/10)

So, you've found c ?

 

[tsaitea]

Yes, but the correct answer for the argument is 2(x+pi/20)

 

[tsaitea]

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!

 

[SammyS]

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.