Trigonometric ratios

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Name

Trigonometric ratios
Figure Sides
TR06.png [math]\text{Let the right triangle } OHA\,[/math]


[math]O=\text{ side adjacent to angle }\theta\,[/math]

[math]A=\text{ side opposite to angle }\theta\,[/math]

[math]H=\text{ hypotenuse}\,[/math]


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



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