- #31
sooyong94
- 173
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Well... I think so...
Solve de Moivre's Theorem: Sin 3x & Cos 3x
- Thread starter sooyong94
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SUMMARY
The discussion focuses on applying de Moivre's Theorem to derive expressions for sin 3x and cos 3x, resulting in the identities cos 3x = cos³ x - 3 cos x sin² x and sin 3x = 3 cos² x sin x - sin³ x. The participants confirm that the tangent identity tan 3x = (3 tan x - tan³ x) / (1 - 3 tan² x) is valid. They also solve the cubic equation t³ - 3t² - 3t + 1 = 0 by identifying roots related to the values of x where tan(3x) = 1, ultimately finding the roots as tan(π/12), tan(5π/12), and tan(9π/12).
PREREQUISITES- Understanding of trigonometric identities
- Familiarity with de Moivre's Theorem
- Knowledge of solving cubic equations
- Basic skills in manipulating algebraic expressions
- Study the derivation of trigonometric identities using de Moivre's Theorem
- Learn how to solve cubic equations using the Rational Root Theorem
- Explore the implications of tangent identities in trigonometric equations
- Investigate the periodic properties of trigonometric functions
Students and educators in mathematics, particularly those studying trigonometry and algebra, as well as anyone interested in solving complex trigonometric equations.
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