Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\tan \alpha =\frac{5}{12}$

Answer 1

Given,

$\tan \alpha =\frac{5}{12}$

Let $\alpha =\angle A$

We know that,

$\tan \alpha =\frac{oppositeSide}{adjacentSide}$

Consider the figure above,

From Pythagoras theorem,

$A{C}^2=A{B}^2+A{C}^2$

$A{C}^2={12}^2+5^2$

$A{C}^2=144+25=169AC=13$

$\sin \alpha =\frac{5}{13}$

$\cos \alpha =\frac{12}{13}$

AC=13$\cos\alpha=\dfrac{adjacent Side}{Hypotenuse}=\dfrac{12}{13}$

$\csc \alpha =\frac{1}{\sin \alpha }=\frac{13}{5}$

$\sec \alpha =\frac{1}{\cos \alpha }=\frac{13}{12}$

$\cot \alpha =\frac{1}{\tan \alpha }=\frac{12}{5}$

csc⁡θ=1sin⁡θ=1513=135