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

b. -1/2

Explanation:

:)

Answer 2

C) √3

tanθ = √3

Explanation:

Step:-1

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

Given that the angle

sinθ =
`(-√(3) )/(2)`

Given that the Opposite side AB =
`√(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 =
`(AB)/(BC) = (√(3) )/(1)`