Solve x in Terms of c: 3x+cos 2x = c

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SUMMARY

The equation 3x + cos(2x) = c cannot be solved analytically for x in terms of c. Forum participants emphasized that while a closed-form solution is not possible, alternative methods exist to find x. The discussion highlighted the importance of understanding the context of the problem, suggesting that clues may be provided in textbooks or class materials to aid in solving the equation. Participants encouraged a deeper exploration of numerical or graphical methods to approach the solution.

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  • Understanding of trigonometric functions, specifically cosine.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of numerical methods for solving equations, such as Newton's method.
  • Basic graphing skills to visualize functions and their intersections.
NEXT STEPS
  • Research numerical methods for solving non-linear equations, focusing on Newton's method.
  • Explore graphical techniques for finding roots of equations using software like Desmos or GeoGebra.
  • Study the properties of the cosine function and its impact on equation behavior.
  • Investigate iterative methods for approximating solutions to equations without closed forms.
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Students tackling non-linear equations, mathematics educators seeking teaching strategies, and anyone interested in numerical analysis or trigonometric problem-solving techniques.

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Homework Statement



3x+cos 2x = c
c is an unknown constant.
how do i solve x in terms of c?
 
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You can not do that analytically.
 
Is there more to the original question?
 
What kind of homework problem is this? If it's a real homework problem you were given some clues in your book or in your class as to how to go about solving for x.

As dirk mentioned, there is no closed form analytic way to solve for x. That doesn't mean that you can't solve for x. There are all kinds of ways to do this. Before we help you, we need to know a bit more about the problem. We don't do your homework for you at this site. We instead help you do own homework.
 

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