Mathematics-Online lexicon: Sine and Cosine

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	Mathematics-Online lexicon:
	Sine and Cosine

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overview

$\displaystyle (\cos t,\sin t), \quad t\in \mathbb{R}$

denotes the coordinates of the vector

rotated by the angle

$\includegraphics[bb=138 550 252 664,clip,height=.25\linewidth]{a_sinuscosinus_bild1.eps}$

$\includegraphics[bb=133 546 461 668,clip,height=.25\linewidth]{a_sinuscosinus_bild2.eps}$

Obviously both of these circular functions are $2\pi$ -periodic and it holds

$\cos t = \sin (t+\pi /2)$
$\cos t = \cos (-t), \quad \sin t = -\sin (-t)$
$\sin^2(t) + \cos^2(t) = 1$

Some special values are

$\begin{displaymath} \begin{array}{\vert c\vert\vert c\vert c\vert c\vert c\vert ... ...& \frac{1}{2}\sqrt{2} & \frac{1}{2} & 0 \\ \hline \end{array}\end{displaymath}$

[Examples] [Links]

automatically generated 4/ 7/2008