# Replicating a cosine graph with sine, given transformations?

Say I have a cos function, $y = 1.2cos(0.503x) + 5$ And say I want to replicate it using sine, so expressing the above function in sine so that it gives "the same wave".

How would I do this? I know I have to find a phase shift, but I don't get the steps on how to do it. Also, please no use of Wolframalpha or the like, because I'll have to do these types of problems in class without them.

• do you just want $1.2\cos(0.503x + \pi/2) + 5 = 1.2\sin(0.503(x + \pi/(2*.503)) + 5?$ – abel Jun 7 '15 at 2:34
• Not sure what you mean... – user164403 Jun 7 '15 at 2:36
• Yes, that is what I want. – user164403 Jun 7 '15 at 2:40

$\cos(x)$ is $\sin(x)$ shifted by $\pi/2$
$$\therefore \sin(x) = \cos(x - \pi/2)$$