Maximum and chnage of sign of a function

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A function is needed that has a maximum at 7Pi/4 and changes sign under the transformation phi -> phi + Pi within the range 0 < phi < 2Pi. The discussion highlights that while it's possible to find a function with a maximum at this point, ensuring it changes sign is crucial. The transformation sin(x + Pi) = -sin(x) is referenced as a method to achieve the sign change. A suggested function is sin(phi - Pi/4), which meets the criteria for both the maximum and sign change. This approach successfully addresses the requirements of the problem.
Physicslad78
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Guys Can anyone help me in this? I need a function (cos or sin) maximum at 7Pi/4 and at the same time changes sign under phi->phi+Pi with 0< phi< 2Pi...Thank you
 
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Do you know how to shift and stretch functions?
 
Yes of course I do and u can find a function that is maximum at 7pi/4 but the problem is how to also make it change sign under phi->phi+Pi...
 
sin(x+ \pi)= -sin(x)

That's no problem at all!
 
Thanks HallsofIvy but the maximum of the function should be at \phi=\frac{7\pi}{4}. I guess the function should be \sin (\phi-\frac{\pi}{4})
 

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