Maximum and chnage of sign of a function

[Physicslad78]

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

 

[qntty]

Do you know how to shift and stretch functions?

 

[Physicslad78]

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...

 

[HallsofIvy]

$$sin(x+ \pi)= -sin(x)$$

That's no problem at all!

 

[Physicslad78]

Thanks HallsofIvy but the maximum of the function should be at $$\phi=\frac{7\pi}{4}$$. I guess the function should be $$\sin (\phi-\frac{\pi}{4})$$