Solve the equation for all solutions in the interval [0, 27t). 10) V2 Cos 2x = 1 %3D

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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Solve the equation for all solutions in the interval [0, 27).
10) /2 cos 2x = 1
Transcribed Image Text:Solve the equation for all solutions in the interval [0, 27). 10) /2 cos 2x = 1
Expert Solution
Concept Used

Given: 2cos2x=1

To find all x values in the interval [0,2π)

The cosine function is positive in the 1st and 4th quadrants.

Step 2

To find the general solution let isolate the cosine function and the value of cosπ4=12 cosine function is positive in first and fourth quadrant using cos2π-x=cosx

2cos2x=1cos2x=12cos2x=cosπ42x=π4x=π8cos2π-π4=cosπ4cos7π4=cos2x7π4=2x7π8=x2x=±2nπ+π4 and ±2nπ+7π4x=±22+π4·2 and ±22+7π4·2x=±nπ+π8 and ±nπ+7π8

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