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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:

 Home | Mathematics | * Finance Calculator * Applied Mathematics * Calculus Primer * 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 Behind Stopping a Car The Mathematics of Pi The Mathematics of Population Increase Share This Page