Question

If θ is an angle in standard position whose terminal side lies in quadrant III and sin θ=-√3/2, find the exact value of the tan θ

Answer 1

Answer:

C) √3

tanθ = √3

Step-by-step explanation:

Step:-1

Given that  θ be an angle in standard position whose terminal side

Given that the angle

                 sinθ = $\frac{-\sqrt{3} }{2}$

Given that the Opposite side  AB = $\sqrt{3}$

                        Hypotensue     AC = 2

Step(ii):-

By using Pythagoras theorem

                        AC² = AB² +BC²

                        BC² = AC² - AB²

                       BC²  = 4 - (√3)²

                               = 4-3

                         BC = 1

    Adjacent side(BC)  = 1

Step(iiI):-

Given that 'θ' lies in the third quadrant so tanθ is positive

                     tanθ = $\frac{AB}{BC} = \frac{\sqrt{3} }{1}$