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Cosine

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

Contents

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)[1]

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):

File:Sin Cos Graph.png

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

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See also

Notes

  1. ↑ Provide illustration.
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