The Inverse Sine and Cosine
Let's take a look at the earlier graph:
Now that we learned about Monotonicity Intervals, we can "split" a section of this function to create the inverse.
The most important part: Both the sine and cosine fluctuate between -1 and 1. We can make a "cut" on that interval for the inverses.
The cosine starts at 1 for x = 0 and is strictly decreasing all the way to x = pi, for which it's equal to -1. So, we have our first monotonicity interval. We'll only consider cos(x) on the following interval:
If at x = 0, cos(x) = 1, and at the very end, x = pi, cos(x) = -1.
What will the inverse do?
Well, if we take cos(x) = 1, its inverse will give back our x for which it's 1, so the inverse of cos(x) for the value 1, gives us our original x = 0.
In the same way, we'll get pi for -1.
Indeed, the inverse cosine is now defined over the closed interval from -1 to 1:
The inverse sine is now defined over the closed interval from -1 to 1: 
Click to move on to The Inverse Tangent