Thread: Intersection of a circular function and a cubic

1. Intersection of a circular function and a cubic

Not really sure how to approach this one analytically, any clues?

x3 +2x = 5cos x

Cheers,

2. Re: Intersection of a circular function and a cubic

You cannot solve for $x$ explicitly, you will need to use a numeric root finding technique, such as Newton's method to approximate the root. This is a method from differential calculus.

3. Re: Intersection of a circular function and a cubic

Oh I see, well I'm not familiar with such a technique so I guess a graphical solution will have to suffice. Thank you Mark!

4. Re: Intersection of a circular function and a cubic

You should find $x\approx0.96707029542400250809$. This is what the computer returns, using a numeric method.