Proof That sin(x + 90) = cos(x)

Here is a circle with the raduis of one:

Lets say an orange line has been raised by angle x. We know that the purple line shown below is equal to cos(x):

Now lets raise the orange line by 90 degrees more:

As you can see, cos(x) and sin(x + 90) are both a. Since they have the same values, we can say that [sin(x + 90) = cos(x)].