# Least squares approximation of a function?

1. Mar 29, 2016

### DerpyPenguin

1. The problem statement, all variables and given/known data
Find the least squares approximation of cos^3(x) by a combination of sin(x) and cos(x) over the interval (0, 2pi)

2. Relevant equations

3. The attempt at a solution
I know how to find a least squares approximation with vectors, but I don't even know how to start with a function? The normal equation wouldn't work here because there are no vectors correct? The answer in the back of the book gives sin (x)+(3/4)cos(x), but I don't even know what that answer means. Please help.

2. Mar 29, 2016

### Simon Bridge

You won't be able to do it by folowing a formula... you need to understand what least squares regression is and apply the principle. The formula for vectors should have been derived for you. Note: cos and sin are vectors.

So if you had an arbitrary vector, $\vec a$ and you needed it in terms of two other vectors $\vec u$ and $\vec v$... how would you go about it?

Last edited: Mar 29, 2016
3. Mar 30, 2016

### LCKurtz

Perhaps you don't know what the answer means because you don't know the definition of least squares approximations for functions. Surely it is in your text. Or looking here: