Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 5 cos3 x = 5 cos x
Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 5 cos3 x = 5 cos x
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
5 cos3 x = 5 cos x
Expert Solution
Step 1
Solution ) 5cos3x = 5cosx
5cos3x - 5cosx = 0
5cosx ( cos2x - 1 ) = 0
cosx ( cos2x - 1 ) = 0
From this cos x = 0 ,
[cos ( 2n + 1)π/2 = 0]
cos2x - 1 = 0
cos2x = 1
cos x ,= 1
[ cos 2nπ = 1 ]
x = 0 , π/2 , π, 3π/2
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