Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\cos \theta =\frac{7}{25}$

Answer 1

Given,

$cos\theta =\frac{7}{25}$

We know that,

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

Consider the figure above,

From Pythagoras theorem,

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

${25}^2=7^2+B{C}^2$

$B{C}^2=625-49=576$

$BC=24$

$\sin \theta =\frac{AdjacentSide}{Hypotenuse}=\frac{24}{25}$

$\csc \theta =\frac{1}{\sin \theta }=\frac{1}{\frac{24}{25}}=\frac{25}{24}$

$\tan \theta =\frac{OppositeSide}{AdjacentSide}=\frac{24}{7}$

$\sec \theta =\frac{1}{\cos \theta }=\frac{1}{\frac{7}{25}}=\frac{25}{7}$

$\cot \theta =\frac{1}{\tan \theta }=\frac{1}{\frac{24}{7}}=\frac{7}{24}$