Register to reply

Approximation of values from non-closed form equation.

Share this thread:
Mar7-14, 07:17 PM
P: 72
Hello everyone, I'm working on a problem and it turns out that this equation crops up:

[tex]1 = cos^{2}(b)[1-(c-b)^{2}][/tex]


[tex]c > \pi[/tex]

Now I'm pretty sure you can't solve for b in closed form (at least I can't), so what I need to do is for some value of c, approximate the value of b to about 5-6 digits of accuracy. I just need tips to head in the right direction. Anything will be useful. Thank you!
Phys.Org News Partner Mathematics news on
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Mar7-14, 07:47 PM
P: 392's_method

Put simply, ##x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}##. Just iterate the formula a few times to get an approximate answer.
Mar8-14, 01:36 AM
P: 759
[tex]1 = cos^{2}(b)[1-(c-b)^{2}][/tex]
[tex]1-cos^{2}(b) = cos^{2}(b)[-(c-b)^{2}][/tex]
[tex]sin^{2}(b) = cos^{2}(b)[-(c-b)^{2}][/tex]
[tex]tan^{2}(b) = -(c-b)^{2}[/tex]
For real solution, positive term = negative term is only possible if they are =0.
Hence the solution is : [tex]c=b=n\pi[/tex]

Mar8-14, 11:44 AM
P: 72
Approximation of values from non-closed form equation.

Oh okay, thanks JJacquelin, I didn't even think to do this.

Register to reply

Related Discussions
Does this differential equation have a closed form? Differential Equations 3
Write a closed form expression for the approximation y(nC)... Calculus & Beyond Homework 7
Quadratic Forms: Closed Form from Values on Basis? Linear & Abstract Algebra 0
Plotting a non-closed form of an equation Math & Science Software 2
Closed-form solutions to the wave equation Quantum Physics 6