Question

If $\cos \theta =\frac{24}{25}$ Find the values of other trigonometric ratios.

Answer 1

In $△ABC$, $\angle B={90}^o$, $\angle C=\theta$
$\therefore {AB}^2={AC}^2-{BC}^2$ ........ (By Pythagoras theorem)
$\therefore x^2={25}^2-{24}^2=625-576=49$
$\therefore x=\sqrt{49}=7$

$\therefore AB=7$
Now, we can write other trigonometric ratios as follows
$\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{7}{25}$

$\tan \theta =\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{7}{24}$

$\csc \theta =\frac{\text{Hypotenuse}}{\text{Opposite side}}=\frac{25}{7}$

$\sec \theta =\frac{\text{Hypotenuse}}{\text{Adjacent side}}=\frac{25}{24}$

$\cot \theta =\frac{\text{Adjacent side}}{\text{Opposite side}}=\frac{24}{7}$