How to Solve a Trig Equation for x with Cosine and Sine Terms

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Homework Help Overview

The problem involves solving a trigonometric equation that combines cosine and sine terms: cos²x + 2sin²x = -1. Participants are exploring methods to manipulate the equation and apply trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin solving the equation, noting the known identity cos²x + sin²x = 1 but questioning its applicability due to the coefficient of 2. Some participants suggest breaking down the equation further or substituting terms to simplify it.

Discussion Status

The discussion is ongoing, with participants providing insights on how to approach the equation. Some have offered suggestions for rewriting the terms, indicating a productive exploration of potential methods without reaching a consensus on a solution.

Contextual Notes

The original problem presents a challenge due to the presence of the coefficient in front of the sine term, which may affect the application of standard trigonometric identities.

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Homework Statement


cos^2x+2sin^2x=-1

Solve for x

Homework Equations





The Attempt at a Solution


I don't really know how to start. I know cos^2x+sin^2x=1 but I don't think I can apply that with the 2 thrown in there.
 
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Observe: cos^2 + 2 sin^2 = (cos^2 + sin^2) + sin^2
 
thank you
 
Or, if it weren't quite that obvious, you could have replaced cos^2(x) with 1- sin^2(x). That is, cos^2(x)+ 2sin^2(x)= (1- sin^2(x))+ 2sin^2(x)= 1+ sin^2(x)= 1.
 

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