Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\cos A$= $\frac{4}{5}$

Answer 1

Given,

$cos$ $A=\frac{4}{5}$

We know that,

$\cos \theta =\frac{adjacentSide}{Hypotenuse}$ $(Here\theta =A)$

Consider the figure above,

From Pythagoras theorem,

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

$5^2=4^2+B{C}^2$

$B{C}^2=25-16=9$

$BC=3$

$\sin \theta =\frac{OppositeSide}{Hypotenuse}=\frac{3}{5}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{1}{\frac{4}{5}}=\frac{5}{4}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{1}{\frac{3}{5}}=\frac{5}{3}$

$\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{4}{3}$