The trigonometric functions are defined with the aid of the unit circle as follows:
The perhaps most important trigonometric formulas from which almost all other trigonometric formulas can be derived are the angle transformation formulas:
- These formulae can be derived by computing the distance between two points on the unit circle with the distanceformula and with the cosinetheorem and then equating them to each other.
- And by direct application of the Pythagorean theorem on the unit circle one obtains the important relation
- connecting sine and cosine.