Question

If sin Θ =- radical 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?

Answer 1

now.. notice the location of θ, is between
`\bf \pi \ \textless \ \theta\ \textless \ (3\pi )/(2)`

that simply means the 3rd quadrant

recall, on the 3rd quadrant, sine is negative and cosine is negative

check the picture, and use the pythagorean theorem to get the missing side of that triangle, or the adjacent, or "a"

once you have all three sides, y,x,r or a,b,c
use those to get cosine and tangent of the angle