Let's take a sine wave ( f(x)= sin(x)) A cosine wave can be represented as sin( pi/2 - x ) Now let's plot both the functions in the same graph: The cosine wave is the sine wave moved 90 degrees to the left. or. The sine wave is the cosine wave moved 90 degrees to the right. We say that the phase difference between the sine and cosine waves is 90 degrees. i.e The cosine and sine waves are out of phase by 90 degrees. This is for a sine and a cosine wave but this idea can be applied to other waves as well. More Answers Below.