Question

If tan x=3/4 and x lies in the third quadrant find sin x

Answer 1

Answer:-

Sin x = 3/5

Step - by - step explanation:-

To find :-

Find sin x

Given:-

$\bf{ \tan(x) = \frac{3}{4} }$

Solution:-

We know that,

$\tan( x) = \frac{perpendicular}{base} = \frac{3}{4}$

By the help of Pythagoras-

$\bf{hypt. = \sqrt{ {perpend.}^{2} + {base}^{2} } } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{9 + 16} = 5$

Now ,we know that,

$\bf{\sin(x) = \frac{perpend.}{hypt.} }\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3}{5}$

Answer 2

$\\ according \: to \: the \: question \: \tan(x \ ) lies \: to \: third \: quadrant \: \\ \tan(x) = \frac{3}{4} \\ in \: oab \\ angle \: a \: = 90 \: degrees \\ by \: phythogarian \: thereom \\ {ob}^{2} = {oa}^{2} + {ab}^{2} \\( { - 4}^{2} ) + ( { - 3}^{2} ) \\ 16 + 9 = 25 \\ {5}^{2} \\ ob = 5 \\ now \: \sin(x) = \frac{ab}{ob} = \frac{ - 3}{5}$