Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\tan \theta =11$

Answer 1

Given,

$tan\theta =\frac{11}{1}$

We know that,

$\tan \theta =\frac{oppositeSide}{adjacentside}$$(Here\theta =A)$

Consider the figure above,

From Pythagoras theorem,

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

$A{C}^2=1^2+{11}^2$

$A{C}^2=1+121=122$

$AB=\sqrt{122}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{1}{11}$

$\cos \theta =\frac{AdjacentSide}{Hypotenuse}=\frac{1}{\sqrt{122}}$

$\sin \theta =\frac{OppositeSide}{Hypotenuse}=\frac{11}{\sqrt{122}}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{1}{\frac{1}{\sqrt{122}}}=\sqrt{122}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{1}{\frac{11}{\sqrt{122}}}=\frac{\sqrt{122}}{11}$