Solve de Moivre's Theorem: Sin 3x & Cos 3x

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Homework Help Overview

The discussion revolves around using de Moivre's Theorem to derive expressions for sin 3x and cos 3x, and subsequently deducing the identity for tan 3x. Participants also explore how to solve the cubic equation t³ - 3t² - 3t + 1 = 0 using the derived identities.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss comparing real and imaginary parts of complex expressions to derive trigonometric identities. Questions arise regarding the domain of x and how to find roots of the cubic equation based on the derived identities.

Discussion Status

The discussion is active, with participants attempting to clarify the relationship between tan(3x) and the roots of the cubic equation. Some guidance has been provided regarding the implications of the derived identities, but there remains uncertainty about specific roots and their verification.

Contextual Notes

Participants are working within the constraints of trigonometric identities and the properties of cubic equations, questioning assumptions about the roots and the domain of the tangent function.

  • #31
Well... I think so...
 
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  • #32
sooyong94 said:
Well... I think so...

Can't think why not. You've found three roots with the trig identity that you correctly got through deMoivre. They all work. Cubic equations have a maximum of three roots. We've disposed of the idea t=1 is one of them. Can't think of what else could go wrong.
 
  • #33
Thanks then. :D
 
  • #34
sooyong94 said:
Thanks then. :D

Very welcome.
 

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