Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$cos\theta =\frac{12}{15}$

Answer 1

Given,

$cos\theta =\frac{12}{15}$

We know that,

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

Consider the figure above,

From Pythagoras theorem,

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

${15}^2={12}^2+B{C}^2$

$B{C}^2=225-144=81$

$BC=9$

$\sin \theta =\frac{AdjacentSide}{Hypotenuse}=\frac{9}{15}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{1}{\frac{9}{15}}=\frac{15}{9}$

$\tan \theta =\frac{OppositeSide}{AdjacentSide}=\frac{9}{12}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{1}{\frac{12}{15}}=\frac{15}{12}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{1}{\frac{9}{12}}=\frac{12}{9}$