Question

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

Answer 1

Given,

$cot\theta =\frac{12}{5}$

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

We know that,

$\tan \theta =\frac{oppositeSide}{adjacentSide}=\frac{AB}{BC}$

Consider the figure above,

From Pythagoras theorem,

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

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

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

$AC=13$

$\sin \theta =\frac{oppositeSide}{Hypotenuse}=\frac{5}{13}$

$\cos \theta =\frac{adjacentSide}{Hypotenuse}=\frac{12}{13}$

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

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