transformation of sine graph

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January 27th 2013, 12:00 PM
minicooper58

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transformation of sine graph

Hi , I need help with the following . The first part is write down the equation of y= f(x) given the sketch attached .
The second part is to sketch the graph of 1+2 f(x - 90)
I don't know if the 180 on the sketch given is correct but i take the sketch given as y=2sin2x
and 1+2 f(x - 90) evaluates to 1-2sin2x . Is this right ?

Thank you
January 27th 2013, 12:14 PM
emakarov

Re: transformation of sine graph

When $x=180^\circ$ , we have $2\sin(2x)=2\sin(360)=0$ , not $-2$ .
January 27th 2013, 12:34 PM
minicooper58

Re: transformation of sine graph

I understand that that at 180 y=2sin2x=0 but has the 180 on the sketch been placed too far to the left .
From observation y=2sin2x would give the minimum as (135,-2) .
What is the equation if you take (180,-2) as the minimum ?
January 27th 2013, 12:54 PM
emakarov

Re: transformation of sine graph

Quote:

Originally Posted by minicooper58

I understand that that at 180 y=2sin2x=0 but has the 180 on the sketch been placed too far to the left .
From observation y=2sin2x would give the minimum as (135,-2) .

Yes, the image is not clear. However, the minimum point seems to the right of the fifth tick on the x-axis. Therefore, if 180 corresponds to the that tick, then the minimum point has to be > 180 and not 135. The digits "180" themselves seem to be located directly above the minimum.

Quote:

Originally Posted by minicooper58

What is the equation if you take (180,-2) as the minimum ?

The first positive minimum point of $\sin(kx)$ is 180 iff $k\cdot180=270$ .
January 27th 2013, 01:00 PM
minicooper58

Re: transformation of sine graph

What would you say the equation of y=f(x) is ?
January 27th 2013, 01:06 PM
emakarov

Re: transformation of sine graph

It's $y=2\sin(kx)$ for some k. The equation to find k is given in post #4. I hope that you understand how this equation arises or that you will ask further questions about it.
January 27th 2013, 01:22 PM
minicooper58

Re: transformation of sine graph

Hi , I understand y=2sinkx is the only possible equation given the sketch but if 180 say should have been the endpoint of the sketch ,
then is the equation y=2sin2x with the minimum at (135,-2)
January 27th 2013, 01:28 PM
emakarov

Re: transformation of sine graph

Quote:

Originally Posted by minicooper58

if 180 say should have been the endpoint of the sketch, then is the equation y=2sin2x with the minimum at (135,-2)

If by the "endpoint of the sketch" you mean "the second positive zero of f(x)," then yes, f(x) = 2sin(2x) has the endpoint at x = 180 and (135, -2) is the minimum.
January 27th 2013, 01:38 PM
minicooper58

Re: transformation of sine graph

notice on the sketch that the positive zero of f(x) is not reached but the sketch starts before 0 , indication possibly that the 180 has been marked in error .
Many thanks for your help . Apologies for the poor sketch .