# Intersection of a circular function and a cubic

• May 1st 2013, 10:46 PM
deSitter
Intersection of a circular function and a cubic
Not really sure how to approach this one analytically, any clues?

x3 +2x = 5cos x

Cheers,
• May 1st 2013, 10:51 PM
MarkFL
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.
• May 1st 2013, 11:34 PM
deSitter
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!
• May 1st 2013, 11:57 PM
MarkFL
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.