sec(θ)=9 with 3π/2<θ<2π, determine tan(θ)

1 answer

3π/2<θ<2π tells you that you are in quad IV
secθ = 9 , then
cosθ = 1/9
I know cosθ = x/r, so x = 1, r = 9
x^2 + y^2 = r^2
1 + y^2 = 81
y^2 = 80
y = - 4√5 , since the angle is in IV

tan θ = y/x = -4√5 / 1 = -4√5