* Trigonometric Relations

Right Triangle Element Names:

Relationship Matrix (angles in radians):

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	opp	adj	hyp	A	B
opp & adj	—	—	$\sqrt{o p p^{2} + a d j^{2}}$	$\tan^{- 1} (\frac{o p p}{a d j})$	$\tan^{- 1} (\frac{a d j}{o p p})$
opp & hyp	—	$\sqrt{h y p^{2} - o p p^{2}}$	—	$\sin^{- 1} (\frac{o p p}{h y p})$	$\cos^{- 1} (\frac{o p p}{h y p})$
adj & hyp	$\sqrt{h y p^{2} - a d j^{2}}$	—	—	$\cos^{- 1} (\frac{a d j}{h y p})$	$\sin^{- 1} (\frac{a d j}{h y p})$
opp & A	—	$\frac{o p p}{\tan (A)}$	$\frac{o p p}{\sin (A)}$	—	$\frac{π}{2} - A$
opp & B	—	$o p p \tan (B)$	$\frac{o p p}{\cos (B)}$	$\frac{π}{2} - B$	—
adj & A	$a d j \tan (A)$	—	$\frac{a d j}{\cos (A)}$	—	$\frac{π}{2} - A$
adj & B	$\frac{a d j}{\tan (B)}$	—	$\frac{a d j}{\sin (B)}$	$\frac{π}{2} - B$	—
hyp & A	$h y p \sin (A)$	$h y p \cos (A)$	—	—	$\frac{π}{2} - A$
hyp & B	$h y p \cos (B)$	$h y p \sin (B)$	—	$\frac{π}{2} - B$	—

Notes:

$\frac{π}{2} radians = 90^{\circ}$

$\sin (A) = \frac{o p p}{h y p}$

$\cos (A) = \frac{a d j}{h y p}$

$\tan (A) = \frac{o p p}{a d j}$

$\sin (B) = \frac{a d j}{h y p}$

$\cos (B) = \frac{o p p}{h y p}$

$\tan (B) = \frac{a d j}{o p p}$

References:

Trigonometry (Wikipedia)

Trigonometry (Wolfram MathWorld)

Trigonometry and precalculus (Khan Academy)

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