Cosine


Definition 1

$$\cos A = \dfrac{\text{adjacent}}{\text{hypotenuse}}$$

Definition 2

THEOREM   

The Maclaurin series of cosine is

$$1 - \dfrac{x^2}{2!} + \dfrac{x^4}{4!} - \dfrac{x^6}{6!} + \dfrac{x^8}{8!} - \dfrac{x^{10}}{10!} + \ldots$$

Proof available

THEOREM    \(\forall a,b \in \mathbb{R} : \cos(a + b) = \cos a \cos b - \sin a \sin b\)

Proof available

COROLLARY    \(\forall a,b \in \mathbb{R} : \cos(a - b) = \cos a \cos b + \sin a \sin b\)

Proof available

Parent topics