Definition:Cosine

Analysis
The real function $$\cos: \mathbb{R} \to \mathbb{R}$$ is defined as:

$$\cos x = \sum_{n=0}^\infty \left({-1}\right)^n \frac {x^{2n}}{\left({2n}\right)!} = 1 - \frac {x^2} {2!} + \frac {x^4} {4!} - \cdots$$

$$\cos x$$ is voiced "cosine (of) $$x$$", or (as written) "cos $$x$$" (pronounced either "coss" or "coz" depending on preference).

Geometry


In the above right triangle, we are concerned about the angle $$\theta$$.

The cosine of $$\angle \theta$$ is defined as being $$\frac {\text{Adjacent}} {\text{Hypotenuse}}$$.