Definition:Cosine

Trigonometry

 * SineCosine.png

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

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

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


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

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

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

Also see

 * Sine, tangent, cotangent, secant and cosecant
 * Basic Properties of Cosine Function
 * Nature of Cosine Function