## Half Range Fourier Series in Hindi #8 How To Study Half Range Sine & Cosine Fourier Series in Hindi

**EVEN FUNCTION**

A function y = f(x) is said to be even, if f(-x) = f(x). The graph of the even function is always symmetrical about the y-axis.

**ODD FUNCTION**

A function y=f(x) is said to be odd, if f(-x) = – f(x). The graph of the odd function is always symmetrical about the origin. For example, the function f(x) = in [-1,1] is even as f(-x) = = f(x) and the function f(x) = x in [-1,1] is odd as f(-x) = -x = -f(x). The graphs of these functions are shown below : 1. If f(x) is even and g(x) is odd, then

â€¢ h(x) = f(x) x g(x) is odd

â€¢ h(x) = f(x) x f(x) is even

â€¢ h(x) = g(x) x g(x) is even

1. If f(x) is even, then bn=0 This is FOURIER COSINE SERIES ao and an is present

2. If f(x) is odd, then ao=an=0 This is FOURIER SINE SERIES the only bn is present.