Trigonometric Ratios in Right Triangle

Given a right triangle ABC.

Sin A

$\sin A = \frac{\text{opposite side}}{\text{hypotenuse}}$


Cos A

$\cos A = \frac{\text{adjacent side}}{\text{hypotenuse}}$


Tan A

$\tan A = \frac{\text{opposite side}}{\text{adjacent side}}$

$\cot A = \frac{\text{adjacent side}}{\text{opposite side}}$

Or as we can see $\tan A = \frac{1}{\cot A}$

Samples

Sin, cos, tan, cot

$\sin A = \frac{a}{c} = \frac{7}{25}$

$\sin B = \frac{b}{c} = \frac{24}{25}$

$\cos A = \frac{b}{c} = \frac{24}{25}$

$\cos B = \frac{a}{c} = \frac{7}{25}$

$\tan A = \frac{a}{b} = \frac{7}{24}$

$\tan B = \frac{b}{a} = \frac{24}{7}$

$\cot A = \frac{b}{a} = \frac{24}{7}$

$\cot B = \frac{a}{b} = \frac{7}{24}$


Sin, cos, tan, cot

$a = c\cdot\sin A$
$a = c \cdot \cos B$
$a = b \cdot \tan A$
$a = b \cdot \cot B$

$b = c\cdot\sin B$
$b = c \cdot \cos A$
$b = a \cdot \tan B$
$b = a \cdot \cot A$

Practice


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