cos 20 + 5cos 0 +3 = 0 [0,2m]

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 38E
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Question

Solve the equation on the indicated interval. 

cos 20 +5cos e +3 = 0
[0,2m]
Transcribed Image Text:cos 20 +5cos e +3 = 0 [0,2m]
Expert Solution
Step 1

Given,

cos2θ + 5cosθ +3 = 0 

We have to find the values of θ in the interval 0,2π 

Step 2

Solving 

cos2θ + 5cosθ +3 = 0

2cos2θ -1 + 5cosθ +3 = 0                                               because cos2θ = 2cos2θ -1

2cos2θ + 5cosθ +2 = 0

2cos2θ + 4cosθ + cosθ +2 = 0

2cosθcosθ +2+ 1cosθ +2 = 0 

2cosθ+1cosθ +2 = 0  

So, 2cosθ+1= 0 or  cosθ +2 = 0

Solving

  cosθ +2 = 0cosθ = -2              

It is discarded because -1cosθ  1 , So, it is not possible.

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