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

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Homework Help Overview

The problem involves solving the equation 1 - 2sinθ - 3cosθsinθ = 0, which falls under the subject area of trigonometric equations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the equation by substituting cosθ with sqrt(1 - sinθ) and also tries replacing 3cosθsinθ with 3cotθ(sinθ)^2, but finds these approaches lead to complex algebra. Other participants question the complexity of the algebra and suggest that it may not be as complicated as perceived.

Discussion Status

Participants are exploring different methods to approach the problem, with some suggesting graphical solutions as an alternative to finding exact answers. There is no explicit consensus on the best method, but guidance has been offered regarding the potential for simpler approaches.

Contextual Notes

There is a mention of whether exact solutions are required, which may influence the approach taken. The original poster expresses concern about the algebraic complexity involved in solving the equation.

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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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