Question

how many values of theta satisfy the quation 3sin^2 + sin theta-2=0

Answer 1

\(3sin^2(\theta)+sin(\theta)-2=0\)

Let x = sin(Θ).

Solve \(3x^2+x-2=0.\)

But really, with no restriction on domain, there are infinite solutions.

Answer 2

3x^2+x−2=0
(3x-2)(x+1) = 0
for zeros, x=2/3 or x=-1
sin(Θ) = 2/3 ----> Θ = arc(sin(2/3)
sin(Θ) = -1 ----> Θ = 270 degrees or 3pi/2