Where can I find the formal way of this formula?

In this link -

Pauls Online Notes : Linear Algebra - Examples of Linear Transformations

When he is talking about 2D rotations, he says -

Now, through a trig formula we can write the equations for **w** as follows,

I was wondering where a formal definition for this formula can be found. Thanks for any help.

Re: Where can I find the formal way of this formula?

What do you mean by the "definition of a formula"? The identities for the sine and cosine of a sum of angles are found here.