Engineering Handbook/Mathematics/Trigonometry

Trigonometry Identities Table

${\sin }^2+{\cos }^2=1$	$1+{\tan }^2={\sec }^2$
$\sin (\frac{\pi }{2}-\theta )=\cos \theta$	$\cos (\frac{\pi }{2}-\theta )=\sin \theta$
$\sec (\frac{\pi }{2}-\theta )=\csc \theta$	$\csc (\frac{\pi }{2}-\theta )=\sec \theta$
$\sin (-\theta )=-\sin \theta$	$\cos (-\theta )=\cos \theta$
$\sin 2\theta =2\sin \theta \cos \theta$	$\cos 2\theta ={\cos }^2-{\sin }^2=2{\cos }^2\theta -1=1-2{\sin }^2\theta$
${\sin }^2\theta =\frac{1-\cos 2\theta }{2}$	${\cos }^2\theta =\frac{1+\cos 2\theta }{2}$
$\sin \alpha +\sin \beta =2\sin (\frac{\alpha +\beta }{2})\cos (\frac{\alpha -\beta }{2})$	$\sin \alpha -\sin \beta =2\cos (\frac{\alpha +\beta }{2})\sin (\frac{\alpha -\beta }{2})$
$\cos \alpha +\cos \beta =2\cos (\frac{\alpha +\beta }{2})\cos (\frac{\alpha -\beta }{2})$	$\cos \alpha -\cos \beta =-2\sin (\frac{\alpha +\beta }{2})\sin (\frac{\alpha -\beta }{2})$
$\sin \alpha \sin \beta =\frac{1}{2}[\cos (\alpha -\beta )-\cos (\alpha +\beta )]$	$\cos \alpha \cos \beta =\frac{1}{2}[\cos (\alpha -\beta )+\cos (\alpha +\beta )]$
$\sin \alpha \cos \beta =\frac{1}{2}[\sin (\alpha +\beta )+\sin (\alpha -\beta )]$	$1+{\cot }^2={\csc }^2$
$e^{j\theta }=\cos \theta +j\sin \theta$	$\cos \theta =\frac{e^{j\theta }+e^{-j\theta }}{2}$
$\tan (\frac{\pi }{2}-\theta )=\cot \theta$	$\cot (\frac{\pi }{2}-\theta )=\tan \theta$
$\tan (-\theta )=-\tan \theta$	$\tan 2\theta =\frac{2\tan \theta }{1-ta{n}^2\theta }$
${\tan }^2\theta =\frac{1-\cos 2\theta }{1+\cos 2\theta }$	$\sin \theta =\frac{e^{j\theta }-e^{-j\theta }}{j2}$

References

1. Trigonometric Identities