Cosine

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

Given the angle $\theta$ of an arc on a unit circle, $\cos \theta$ 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).

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

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

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

Formulae

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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