The value of [tex]sin(\theta)[/tex] will be [tex]-\frac{3}{5}[/tex]
Explanation
Given that, [tex]tan(\theta)= \frac{3}{4}[/tex]
According to the below diagram, [tex]tan(\theta)= \frac{AB}{BO}[/tex]
As, [tex]\theta[/tex] is in quadrant III , so AB = -3 and BO = -4
Now according to the Pythagorean theorem.....
[tex]AO^2= AB^2+BO^2\\ \\ AO^2= (-3)^2+(-4)^2\\ \\ AO^2= 9+16=25\\ \\ AO=\sqrt{25}=5[/tex]
Thus, [tex]sin(\theta)= \frac{opposite}{hypotenuse}=\frac{AB}{AO}= -\frac{3}{5}[/tex]
