Trigonometric functions

In high school or university, you likely studied trigonometry and encountered the sine, cosine, and tangent functions. More important to us are the sine and cosine functions, which you will encounter often and which we will look at here. These functions can be seen in the following image:

Here, sine is  and cosine is _.

The sine and cosine functions are related, and the derivative will show us how. 

If , then . However, if , then . 

The derivatives create a loop, which we can see as follows: