Question 1098977
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<pre>
Introduce new variable x = {{{cos(theta)}}}.

Then your equation will take the form

{{{2x^2 + 3x +1}}} = 0.


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

{{{x[1,2]}}} = {{{(-3 +- sqrt(3^2 - 4*2*1))/(2*2)}}} = {{{(-3 +- 1)/4}}}.


1)  Case 1:  {{{x[1]}}} = {{{(-3+1)/4}}} = {{{-1/2}}}  ====>  {{{cos(theta)}}} = {{{-1/2}}} ====>  {{{theta}}} = {{{2pi/3} + 2k*pi}}  or  {{{theta}}} = {{{4pi/3+2k*pi}}}.


2)  Case 2:  {{{x[2]}}} = {{{(-3-1)/4}}} = -1  ====>  {{{theta}}} = {{{pi}}} + {{{2k*pi}}}.


<U>Answer</U>.  The solutions are  {{{2pi/3+2k*pi}}}, {{{pi+2k*pi}}}  and  {{{4pi/3+2k*pi}}}.
</pre>


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To see many other solved problems on trigonometry equations and to learn more about this subject, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-simple-problems-on-trigonometric-equations.lesson>Solving simple problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-typical-problems-on-trigonometric-equations.lesson>Solving typical problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-more-complicated-problems-on-trigonometric-equations.lesson>Solving more complicated problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solved-problems-on-trigonometric-equations.lesson>Solving advanced problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Proving-Trigonometry-identities.lesson>Proving Trigonometry identities</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/OVERVIEW-of-lessons-on-calculating-trig-functions-and-solving-trig-equations.lesson>OVERVIEW of lessons on calculating trig functions and solving trig equations</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Trigonometry: Solved problems</U>". 



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.