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Trigonometric Relations

A concise summary of trigonometric equations.

Right Triangle Element Names:

### H a v e

opp
hyp
A
B
opp & adj $\displaystyle \sqrt{opp^2+adj^2}$ $\displaystyle \tan^{-1}(\frac{opp}{adj})$ $\displaystyle \tan^{-1}(\frac{adj}{opp})$
opp & hyp $\displaystyle \sqrt{hyp^2-opp^2}$ $\displaystyle \sin^{-1}(\frac{opp}{hyp})$ $\displaystyle \cos^{-1}(\frac{opp}{hyp})$
adj & hyp $\displaystyle \sqrt{hyp^2-adj^2}$ $\displaystyle \cos^{-1}(\frac{adj}{hyp})$ $\displaystyle \sin^{-1}(\frac{adj}{hyp})$
opp & A $\displaystyle \frac{opp}{\tan(A)}$ $\displaystyle \frac{opp}{\sin(A)}$ $\displaystyle \frac{\pi}{2} - A$
opp & B $\displaystyle opp \, \tan(B)$ $\displaystyle \frac{opp}{\cos(B)}$ $\displaystyle \frac{\pi}{2} - B$
adj & A $\displaystyle adj \, \tan(A)$ $\displaystyle \frac{adj}{\cos(A)}$ $\displaystyle \frac{\pi}{2} - A$
adj & B $\displaystyle \frac{adj}{\tan(B)}$ $\displaystyle \frac{adj}{\sin(B)}$ $\displaystyle \frac{\pi}{2} - B$
hyp & A $\displaystyle hyp \, \sin(A)$ $\displaystyle hyp \, \cos(A)$ $\displaystyle \frac{\pi}{2} - A$
hyp & B $\displaystyle hyp \, \cos(B)$ $\displaystyle hyp \, \sin(B)$ $\displaystyle \frac{\pi}{2} - B$

Notes:

• $\displaystyle \frac{\pi}{2} \text{radians} = 90^{\circ}$

• $\displaystyle \sin(A) = \frac{opp}{hyp}$

• $\displaystyle \cos(A) = \frac{adj}{hyp}$

• $\displaystyle \tan(A) = \frac{opp}{adj}$

• $\displaystyle \sin(B) = \frac{adj}{hyp}$

• $\displaystyle \cos(B) = \frac{opp}{hyp}$

• $\displaystyle \tan(B) = \frac{adj}{opp}$

References:

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