Trigonometric ratios

Name

Trigonometric ratios
Figure Sides
$\text{Let the right triangle } OHA\,$

$O=\text{ side adjacent to angle }\theta\,$

$A=\text{ side opposite to angle }\theta\,$

$H=\text{ hypotenuse}\,$

Trigonometric ratios
Name of Ratio Abbreviation Explicit Formula Formula Memory Aid
$\text{sine of }\theta\,$ $\sin \theta\,$ $\sin \theta=\frac{\text{side opposite to } \theta}{hypotenuse}$ $\sin \theta=\frac{O}{H}$ $\text {SOH}\,$
$\text{cosine of }\theta\,$ $\cos \theta\,$ $\cos \theta=\frac{\text{side adjacent to } \theta}{hypotenuse}$ $\cos \theta=\frac{A}{H}$ $\text {CAH}\,$
$\text{tangent of }\theta\,$ $\tan \theta\,$ $\tan \theta=\frac{\text{side opposite to } \theta}{\text{side adjacent to } \theta}$ $\tan \theta=\frac{O}{A}$ $\text {TOA}\,$
$\text{cotangent of }\theta\,$ $\cot \theta\,$ $\cot \theta=\frac{\text{side adjacent to } \theta}{\text{side opposite to } \theta}$ $\cot \theta=\frac{A}{O}$ 
$\text{secant of }\theta\,$ $\sec \theta\,$ $\sec\theta=\frac{\text{hypotenuse}}{\text{side adjacent to } \theta}$ $\sec \theta=\frac{H}{A}$ 
$\text{cosecant of }\theta\,$ $\csc \theta\,$ $\csc \theta=\frac{hypotenuse}{\text{side opposite to } \theta}$ $\csc \theta=\frac{H}{O}$ 

Usage

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