# Periodic Function

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• Mar 13th 2014, 03:48 PM
nycmath
Periodic Function
The picture shows a portion of the graph of the periodic function
f(x) = sin(1 + sinx). Find the x-coordinates of the turning points P, Q, and R. Round the answers to three decimal places. Hint: The x-coordinate of Q is halfway between the x-coordinates of P and R.
• Mar 13th 2014, 04:06 PM
romsek
Re: Periodic Function
these are all local minima or maxima so set the derivative equal to zero an solve for x. You'll get a few solutions and you should be able to eyeball the correct ones.
• Mar 13th 2014, 04:55 PM
Plato
Re: Periodic Function
Quote:

Originally Posted by nycmath
The picture shows a portion of the graph of the periodic function
f(x) = sin(1 + sinx). Find the x-coordinates of the turning points P, Q, and R. Round the answers to three decimal places. Hint: The x-coordinate of Q is halfway between the x-coordinates of P and R.

Look at this graph.
plot sin(1+sin(x)), -2 to 6 - Wolfram|Alpha
• Mar 13th 2014, 08:01 PM
nycmath
Re: Periodic Function
Thank you everyone.
• Mar 14th 2014, 09:47 AM
johng
Re: Periodic Function
Hi,
I hope the attached drawing helps. In particular, 2 of the critical points (turning points) are symmetrically located about $\pi/2$.

Attachment 30416
• Mar 14th 2014, 10:30 AM
nycmath
Re: Periodic Function
Thank you, johng.