How do I solve the Sin 3x equation?

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Discussion Overview

The discussion revolves around solving the equation sin(3x) = 3 sin(x) - 4 sin^3(x). Participants explore different methods to approach this trigonometric equation, including the use of angle addition formulas.

Discussion Character

  • Exploratory, Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to begin solving the equation.
  • Another participant suggests starting with the identity sin(3x) = sin(2x + x).
  • A subsequent reply indicates progress by expanding sin(3x) using the angle addition formula, resulting in sin(3x) = sin(2x)cos(x) + cos(2x)sin(x).
  • Further clarification is sought regarding the expressions for sin(2x) and cos(2x).
  • One participant thanks others for their assistance, indicating some level of resolution in their understanding.

Areas of Agreement / Disagreement

The discussion shows a progression of ideas, but no consensus is reached on a complete solution to the equation. Participants are collaboratively exploring the problem without a definitive conclusion.

Contextual Notes

Participants have not fully defined sin(2x) and cos(2x), which may affect the next steps in solving the equation.

Who May Find This Useful

Students or individuals interested in trigonometric equations, particularly those seeking collaborative problem-solving approaches in mathematics.

thenewbosco
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no clue how to start this:

show

sin 3x = 3 sin x - 4 sin^3 x
 
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How to start this: sin(3x) = sin(2x+x)
 
right so after doing this i get

sin 3x = sin2x(cos x) + (cos2x)(sin x)

whats next
 
sin(2x)=...?
cos(2x)=...?
 
thanks for the help i got this and the others
 

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