Step By Step Calculus » 6.1 - Right Triangle Trigonometry

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Synopsis
Trigonometric Functions based on Right Triangle: Earlier we defined trigonometric functions in terms of the unit circle. However all six trigonometric functions can also be interpreted as ratios of appropriate sides of a right angle triangle. Considering the right angle triangle shown in the following picture,

we have
\displaystyle \textbf{(SOHCAHTOA) }\qquad \sin \theta =\frac{\text{opp}}{\text{hyp}}, \ \ \cos \theta =\frac{x}{r}=\frac{\text{adj}}{\text{hyp}}, \ \ \tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\text{opp}}{\text{adj}}
\displaystyle \textbf{(SOHCAHTOA) }\qquad \sin \theta =\frac{\text{opp}}{\text{hyp}}, \ \ \cos \theta =\frac{x}{r}=\frac{\text{adj}}{\text{hyp}}, \ \ \tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\text{opp}}{\text{adj}}
\displaystyle \textbf{(CHOSHACAO) }\qquad \csc \theta =\frac{1}{\sin \theta }=\frac{\text{hyp}}{\text{opp}},\ \ \sec \theta =\frac{1}{\cos \theta }=\frac{\text{hyp}}{\text{adj}}\ \ \cot \theta =\frac{\cos \theta }{\sin \theta }=\frac{\text{adj}}{\text{opp}}.
\displaystyle \textbf{(CHOSHACAO) }\qquad \csc \theta =\frac{1}{\sin \theta }=\frac{\text{hyp}}{\text{opp}},\ \ \sec \theta =\frac{1}{\cos \theta }=\frac{\text{hyp}}{\text{adj}}\ \ \cot \theta =\frac{\cos \theta }{\sin \theta }=\frac{\text{adj}}{\text{opp}}.