Cosine

This article page is a stub, please help by expanding it.

The cosine of an angle $\scriptstyle \theta \,$, denoted as $\scriptstyle \cos \theta \,$, is one of the most important [circular] trigonometric functions.

Given the angle $\scriptstyle \theta \,$ of an arc on a unit circle, $\scriptstyle \cos \theta \,$ is the length of the side on a right triangle going along a line along $x=0$ (the other two sides being a side opposing a vertex coinciding with the center of the circle and hypotenuse).

(PLACEHOLDER FOR IMAGE) 

Per the Pythagorean theorem, $\scriptstyle (\sin \theta )^{2}+(\cos \theta )^{2}\,=\,1\,$.

The following graph shows the sine and cosine functions graphed together (sine is in red, cosine in blue):

Taylor series expansion

The Taylor series expansion of the cosine function is

$\cos x=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n)!}}x^{2n}=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+\cdots .\,$

Formulae

(...)

See also

• For the decimal expansions of the cosine of 89 to 1 degrees, see Sine#Table of sine and cosine values.
• {{cos}} mathematical function template