Solve for Theta: Equilibrium of a Particle

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SUMMARY

The discussion focuses on solving the equation for theta in the context of particle equilibrium, specifically the equation $\frac{\tan(\theta)(\sqrt{5-4\cos(\theta)}-1)}{\sqrt{5-4\cos(\theta)}}=\frac{10}{60}$. Participants emphasize the complexity of manipulating the equation, suggesting the substitution of $\tan \theta = \frac{\sin \theta}{\cos \theta}$ and the use of trigonometric identities to simplify the problem. The need for verification of the equation's correctness is also highlighted, indicating the importance of accuracy in mathematical problem-solving.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent and cosine.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of particle equilibrium concepts in physics.
  • Ability to apply trigonometric identities in problem-solving.
NEXT STEPS
  • Study the derivation and application of trigonometric identities.
  • Learn methods for solving nonlinear equations in trigonometry.
  • Explore the principles of particle equilibrium in physics.
  • Practice solving similar equations involving trigonometric functions.
USEFUL FOR

Students and professionals in physics and engineering, particularly those dealing with mechanics and equilibrium problems, will benefit from this discussion.

Drain Brain
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solve for theta

$\frac{\tan(\theta)(\sqrt{5-4\cos(\theta)}-1)}{\sqrt{5-4\cos(\theta)}}=\frac{10}{60}$

I have already tried my best solving this eqn but still couldn't get it. FYI getting that equation already took me a lot of work. Now I'am on the last piece of the problem I am solving which is to solve for theta. So please kindly tell me how to go about it. Thanks! By the way the problem is about equlibrium of a particle. Thanks!
 
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Well, you say that it took a lot of time for you to get this equation. So, I request you to cross check if the equation is correct.
 
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I think puttiing $\tan \theta = \dfrac{\sin \theta}{\cos \theta}$ shall comlpicate. I would square it and put $\tan^2\theta= \dfrac{ 1}{\cos ^2 \theta} -1$ then solve for $\cos \theta$

By the way could you mention what you have tried
 

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