Question

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

Answer 1

The value of
`sin(\theta)` will be
`-(3)/(5)`

Step-by-step explanation

Given that,
`tan(\theta)= (3)/(4)`

According to the below diagram,
`tan(\theta)= (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=√(25)=5`

Thus,
`sin(\theta)= (opposite)/(hypotenuse)=(AB)/(AO)= -(3)/(5)`