Question

If $\tan \theta =\frac{3}{4}$, find the $sine,cosine,versine$, and $cosecant$ of $\theta$

Answer 1

$\tan \theta =\frac{3}{4}$ [ Given ]

We know, $\tan \theta =\frac{oppositeside}{adjacentside}$

$\therefore$ Opposite side $=3$ and Adjacent side $=4$

$\Rightarrow$ $(Hypotenuse{)}^2=(Oppositeside{)}^2+(Adjacentside{)}^2$

$=(3{)}^2+(4{)}^2$

$=9+16$

$=25$

$\therefore$ Hypotenuse $=5$

$\Rightarrow$ $\sin \theta =\frac{Oppositeside}{Hypotenuse}=\frac{3}{5}$

$\Rightarrow$ $\cos \theta =\frac{Adjacentside}{Hypotenuse}=\frac{4}{5}$

$\Rightarrow$ $versin\theta =1-\cos \theta =1-\frac{4}{5}=\frac{1}{5}$

$\Rightarrow$ $\csc \theta =\frac{Hypotenuse}{oppositeside}=\frac{5}{3}$