Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\sin \theta =\frac{11}{15}$

Answer 1

Given,

$sin\theta =\frac{11}{15}$

Let $\theta =\angle A$

We know that,

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

Consider the figure above,

From Pythagoras theorem,

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

${15}^2=A{B}^2+{11}^2$

$A{B}^2=225-121=104$

$AB=2\sqrt{26}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{15}{11}$

$\cos \theta =\frac{AdjacentSide}{Hypotenuse}=\frac{2\sqrt{26}}{15}$

$\tan \theta =\frac{OppositeSide}{AdjacentSide}=\frac{11}{2\sqrt{26}}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{1}{\frac{2\sqrt{26}}{15}}=\frac{15}{2\sqrt{26}}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{1}{\frac{11}{2\sqrt{26}}}=\frac{2\sqrt{26}}{11}$