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Trigonometric Relations

A concise summary of trigonometric equations.

Copyright © 2009, Paul LutusMessage Page

Right Triangle Element Names:
Relationship Matrix (angles in radians):

### H a v e

opp
adj
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:

 Home | Mathematics | * Consumer Loan Calculator * Applied Mathematics * Calculus * Finance Calculator * Is Mathematics a Science? * Maxima * Sage * Trigonometric Relations * Unit Conversions Area of an Irregular Polygon Binomial Probability Equities Myths Graphinity Graphitude Interactive LaTeX Editor Introduction to Statistics Mandelbrot Set Peak People Polygon Calculator Polynomial Regression Data Fit Polynomial Regression Data Fit (Java version) Prime Numbers Quadratic Equation Solver Randomness Signal Processing The Mathematics of Pi The Mathematics of Population Increase The Physics Behind Stopping a Car Why PDF? Share This Page