Solving 2n.Cos^2(n)=1000 - Tips & Tricks

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SUMMARY

The equation 2n.Cos^2(n)=1000 cannot be solved using elementary functions, necessitating numerical methods for solutions. Participants in the discussion highlighted the use of Wolfram Alpha for obtaining solutions, while also suggesting approximation techniques such as interval halving and Newton's method for further exploration. The consensus is that traditional algebraic manipulation is insufficient for this problem, emphasizing the need for computational tools in solving complex trigonometric equations.

PREREQUISITES
  • Understanding of trigonometric identities, particularly cosine and sine functions.
  • Familiarity with numerical methods, specifically Newton's method and interval halving.
  • Basic knowledge of algebraic manipulation and quadratic equations.
  • Experience with computational tools like Wolfram Alpha for solving equations.
NEXT STEPS
  • Research numerical methods for solving transcendental equations, focusing on Newton's method.
  • Explore the capabilities of Wolfram Alpha for solving complex mathematical problems.
  • Study interval halving techniques and their applications in numerical analysis.
  • Learn about trigonometric function properties and their implications in solving equations.
USEFUL FOR

Students, mathematicians, and educators dealing with trigonometric equations, as well as anyone interested in numerical analysis and computational problem-solving techniques.

dirtyaldante
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Homework Statement



Solve for n:

2n.Cos^2(n)=1000

The Attempt at a Solution



So, I think there's a substitution involved here. I tried to rearrange cosine in terms of sine to make it into a quadratic but that didn't work. I've gone through all the table trig identities. I've had other ideas but it's all come to bubkiss. Wolfram equation solver spat out a solution for n but that's not really the point...

Can anybody shed any light on this?
 
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If can't be solved in terms of elementary functions. Your best bet is to find a numerical solution, so either take Wolfram's word for it or solve it using some approximation technique such as halving the interval or Newton's method.
 

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