Fourier Series for Odd and Even Functions Even Functions Deﬁnition: A function f(x) is said to be even if f(-x) = f(x). e.g. x2, cosx are even function Graphically, an even function is symmetrical about y-axis Even Functions Cont. The examples of even functions are: Even Functions Cont. When function is even: When f(x) is an even function then f(x) sinx is an odd function Odd Functions Deﬁnition: A function f(x) is said to be even if f(-x)=-f(x). e.g. sin x, are odd functions. Graphically, an even function is symmetrical about the origion. Odd Functions When f(x) is an odd function then f(x)cosnx is an odd function and f(x)sinnx is an even function. Therefore, EXAMPLE: EVEN EXAMPLE: EVEN EXAMPLE: EVEN EXAMPLE: EVEN EXAMPLE: ODD EXAMPLE: ODD