Definition:Cosine

Analysis
The real function $$\cos: \R \to \R$$ 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

 * SineCosine.png

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

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

Historical Note
The symbology $$\cos$$ was invented by William Oughtred in his 1657 work Trigonometrie.

Also see

 * Sine, tangent, cotangent, secant and cosecant.