SOLUTION: Find all degree solutions. (Enter your answers as a comma-separated list. Let k be any integer.) 2 cos^2 5θ + 3 cos 5θ + 1 = 0

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Question 1098977: Find all degree solutions. (Enter your answers as a comma-separated list. Let k be any integer.)
2 cos^2 5θ + 3 cos 5θ + 1 = 0

Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
Introduce new variable x = .

Then your equation will take the form

 = 0.


It is a quadratic equation. Apply the quadratic formula to solve it:

 =  = .


1)  Case 1:   =  =   ====>   =  ====>   =  = .


2)  Case 2:   =  = -1  ====>   =  + .


Answer.  The solutions are  ,   and  .


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To see many other solved problems on trigonometry equations and to learn more about this subject, look into the lessons
    - Solving simple problems on trigonometric equations
    - Solving typical problems on trigonometric equations
    - Solving more complicated problems on trigonometric equations
    - Solving advanced problems on trigonometric equations
    - Proving Trigonometry identities
    - OVERVIEW of lessons on calculating trig functions and solving trig equations
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Trigonometry: Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



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