Mack1997 Mack1997
  • 25-05-2018
  • Mathematics
contestada

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

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Sicista Sicista
  • 24-09-2018

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]


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