Solving 1 - 2sinθ - 3cosθsinθ = 0: Algebra or Easy Way?

[jaredmt]

Homework Statement

1 - 2sinθ - 3cosθsinθ = 0

Homework Equations

The Attempt at a Solution

first i replaced cosθ with sprt(1 - sinθ) but that appears to give me a crazy algebra problem.
then i tried replacing 3cosθsinθ with 3cotθ(sinθ )^2 but that doesn't get me anywhere.

i must be forgetting something. is there an easy way to solve this? or am I just going to have to deal with the excessive algebra?

 

[Hurkyl]

that appears to give me a crazy algebra problem.

What's so crazy about it? It looks uncomplicated to me, and of the type you've probably spent an entire chapter (or at least section of a chapter) practicing how to solve.

(By the way, don't forget that (1 - sin² θ) has two square roots)

(By the way, answers required to be exact?)

 

[jaredmt]

well i just came across this in Engineering Mechanics. I thought maybe there was an easier way that I forgot about. I guess not, I'll be able to do it, its just gunna be a pain lol

 

[RTW69]

Do you need an exact solution? If not just graph the equation and identify the zero's. There appear to be 2 soln's between 0 and 2pi.