1. trig equation

I want to know if there is an analytical solution for equations of this type:

cos(x) = x^2

This is very easy to solve with the graphic calculator by plotting the two graphs and finding the intersection. In this case x= 0.8241 or -0.8241.

Thank you.

2. Re: trig equation

Originally Posted by BERMES39
I want to know if there is an analytical solution for equations of this type:

cos(x) = x^2

This is very easy to solve with the graphic calculator by plotting the two graphs and finding the intersection. In this case x= 0.8241 or -0.8241.

Thank you.
I have never seen any analytic solution of these types of equations although i don't know if someone can prove that no analytic solution exists. I don't know how to DEFINE 'analytic solution' for that matter.

3. Re: trig equation

do you know about Newton Ramphson's method. I think it will be helpful

4. Re: trig equation

Thank you, but I am not familiar with the Newton Ramphson's method, and don't seem to find it in my references. Could you explain what this method is?

Your help is appreciated.

5. Re: trig equation

Originally Posted by BERMES39
Thank you, but I am not familiar with the Newton Ramphson's method, and don't seem to find it in my references. Could you explain what this method is?

Your help is appreciated.
It is Newton-Raphson's method (use Google if you want to find out more). I doubt you are expected to use it. Use technology to get an approximate solution to the equation (to the desired accuracy), it cannot be solved exactly.