How to solve this trig equation in radians 2sin^2(x) + sin(x) - 1=0

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Homework Help Overview

The discussion revolves around solving the trigonometric equation 2sin²(θ) + sin(θ) - 1 = 0 for all values of θ in the interval [0, 2π] in radians. Participants are exploring methods to approach this problem, which involves understanding trigonometric identities and quadratic equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants suggest using trigonometric identities and substituting sin(θ) with a variable to simplify the equation. Others express confusion about the problem's requirements and seek further clarification on the steps involved.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the problem and explore different approaches. Some guidance has been offered regarding substitution and the quadratic form of the equation, but there is still uncertainty among participants about the overall process.

Contextual Notes

Participants have noted a lack of familiarity with the material, indicating that this problem may be part of a review sheet from a previous course. There is also mention of needing to solve for angles within a specific interval, which adds a layer of complexity to the discussion.

UrbanXrisis
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I just got a review sheet in math that contain questions that I don't know how to do from last year. ONe asks to solve for all values of theta of [0,2pi] in radians: 2sin^2(theta)+sin(theta)-1=0

any ideas?
 
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Use
[tex]sin\ 2\theta = 2\ sin\ \theta\ cos\ \theta[/tex]
[tex]sin^2\ \theta + cos^2\ \theta = 1[/tex]
 
that confuses me more. I have no clue what the question is even asking, I think I forgot all my math. Could you give a longer explanation?
 
Let [tex]sin\ \theta\ = x[/tex]

Then your original equation now looks like [tex]2x^2 + x - 1 = 0[/tex].

Solve the quadratic equation. Once you do that, the rest should be easy.
 
UrbanXrisis said:
that confuses me more. I have no clue what the question is even asking, I think I forgot all my math. Could you give a longer explanation?

The question is asking for which angles in a 0 to 2pi interval satisfy that equation.

-Cyclovenom
 
forget about what i have said. use recon's suggestion and understand cyclovenom's point.
 

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