# Can fourier sine series approximate even functions?

1. Sep 23, 2015

I am learning Fourier series and have come across the sine, cosine, and imaginary exponential expressions. To my knowledge, these individual terms form a basis since they are all orthogonal to each other. I am just wondering: can a Fourier sine series be used to model a purely even function, such as cosx or $x^2$? Are there any limitations with using a fourier sine series on even functions?

2. Sep 23, 2015

### axmls

No. The coefficient of the sine term is zero for an even function. If $f$ is even, and taking into account that the product of an even and odd function is odd, then you can see that the calculation for the sine coefficient yields 0 when you use the formula for the coefficients.