Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\tan \theta =\frac{8}{15}$

Answer 1

Given,

$tan\theta =\frac{8}{15}$

Let, $\theta =\angle A$

We know that,

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

Consider the figure above,

From Pythagoras theorem,

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

$A{C}^2={15}^2+8^2$

$A{C}^2=225+64=289$

$AC=17$

$\sin \theta =\frac{oppositeSide}{Hypotenuse}=\frac{8}{17}$

$\cos \theta =\frac{AdjacentSide}{Hypotenuse}=\frac{15}{17}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{1}{\frac{8}{17}}=\frac{17}{8}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{1}{\frac{15}{17}}=\frac{17}{15}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{15}{8}$