How do I solve the Sin 3x equation?

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SUMMARY

The discussion focuses on solving the equation sin(3x) = 3 sin(x) - 4 sin^3(x). The user correctly identifies that sin(3x) can be expressed as sin(2x + x) and begins to apply the sine addition formula. The next steps involve determining the values of sin(2x) and cos(2x) to progress further in solving the equation.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the sine addition formula.
  • Knowledge of double angle formulas for sine and cosine.
  • Familiarity with polynomial equations involving trigonometric functions.
  • Basic algebraic manipulation skills to simplify expressions.
NEXT STEPS
  • Study the sine addition formula in detail to apply it effectively.
  • Learn the double angle formulas: sin(2x) = 2 sin(x) cos(x) and cos(2x) = cos^2(x) - sin^2(x).
  • Explore methods for solving polynomial equations involving trigonometric functions.
  • Practice solving similar trigonometric equations to reinforce understanding.
USEFUL FOR

Students studying trigonometry, mathematics enthusiasts, and anyone looking to deepen their understanding of trigonometric equations and identities.

thenewbosco
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no clue how to start this:

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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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