Can you help me with this trigonometry question

Questions is:
find to the nearest hundredth all the values of Θ in the interval pi less then or equal to Θ less then or equal to 2pi


2sin^2Θ+3cosΘ-3=0


now i know that sin^2Θ-1=cos^2
but how do i solve this problem?

That's right, now sub in cos(theta)^2 into the equation:
2cos(theta)^2 + 3cos(theta) - 2 = 0

Let x = cos(theta) and plug in:
2x^2 + 3x - 3 = 0

Solve for x using quadratic equation.
x=.5, x=-2

Earlier, we said x = cos(theta), which means
theta = arccos(x)
theta = .5

substitute sin^2 = 1 - cos^2 , then solve the quadratic equation
(cosΘ - 1)(2cosΘ - 1) = 0 ----> cosΘ = 1 ----> Θ = ...
and cosΘ = 1/2 ---> Θ = ...