Question

Find sin θ if θ is in Quadrant III and tan θ = 3/4.

Answer 1

The value of $sin(\theta)$ will be $-\frac{3}{5}$

Explanation

Given that, $tan(\theta)= \frac{3}{4}$

According to the below diagram, $tan(\theta)= \frac{AB}{BO}$

As, $\theta$ is in quadrant III , so AB = -3 and BO = -4

Now according to the Pythagorean theorem.....

$AO^2= AB^2+BO^2\\ \\ AO^2= (-3)^2+(-4)^2\\ \\ AO^2= 9+16=25\\ \\ AO=\sqrt{25}=5$

Thus, $sin(\theta)= \frac{opposite}{hypotenuse}=\frac{AB}{AO}= -\frac{3}{5}$