# Approximation of values from non-closed form equation.

1. Mar 7, 2014

### Legaldose

Hello everyone, I'm working on a problem and it turns out that this equation crops up:

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

where

$$c > \pi$$

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!

2. Mar 7, 2014

3. Mar 8, 2014

### JJacquelin

$$1 = cos^{2}(b)[1-(c-b)^{2}]$$
$$1-cos^{2}(b) = cos^{2}(b)[-(c-b)^{2}]$$
$$sin^{2}(b) = cos^{2}(b)[-(c-b)^{2}]$$
$$tan^{2}(b) = -(c-b)^{2}$$
For real solution, positive term = negative term is only possible if they are =0.
Hence the solution is : $$c=b=n\pi$$

4. Mar 8, 2014

### Legaldose

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

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