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-$(\frac{ \sqrt{3} }{2})$²=-√(1-$\frac{3}{4})$=- √0.25=- 0.5
tgθ=$\frac{sin \alpha }{cos \alpha }$=  - $\frac{ \sqrt{3} }{2}: (- 0.5)$=√3


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