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

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The equation 1 - 2sinθ - 3cosθsinθ = 0 presents a challenge in finding a straightforward solution. Initial attempts to simplify using substitutions for cosθ led to complex algebraic expressions. Some participants suggest that the problem is manageable and aligns with typical practice problems. An alternative approach mentioned is to graph the equation to identify solutions, noting that there are two solutions between 0 and 2π. The discussion highlights the balance between algebraic methods and graphical solutions in tackling trigonometric equations.
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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?
 
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jaredmt said:
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?)
 
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
 
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.
 

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