Question

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

Answer 1

Step-by-step explanation:

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}

Answer 2

Answer:

-3/5

Step-by-step explanation:

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