Question

If sin Θ = -square root3/2 and π < Θ < 3pi/2 , what are the values of cos Θ and tan Θ

Answer 1

π < θ < 3pi/2, so θ ∈ 3 quadrant,
so cosθ<0, tg θ>0

we know that sin²θ+cos²θ=1

cosθ=-√(1-sin²θ)=-√1-
`(( √(3) )/(2))`²=-√(1-
`(3)/(4))`=- √0.25=- 0.5
tgθ=
`(sin \alpha )/(cos \alpha )`= -
`( √(3) )/(2): (- 0.5)`=√3


P.s. θ=
`\alpha`, i can't put θ in formula, sorry