. (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate real and imag- inary parts to derive the identities cos x = } cos x + cos 3x, sin x = } sin x – sin 3.x. (b) Use the result of part (a) to find a general solution of y" + 4y = cos³ x.
. (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate real and imag- inary parts to derive the identities cos x = } cos x + cos 3x, sin x = } sin x – sin 3.x. (b) Use the result of part (a) to find a general solution of y" + 4y = cos³ x.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 44E
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