Problem 2-6: Odd and Even Functions


Which one of the following functions are even or odd or neither?
a)  \sin(x)
b)  \cos(x)
c)  \sin(x)\cos(x)
d)  x \sin(x)
e)  x^2
f)  \sin(x) + \cos(x)

Recall that a function is said to be even if  f(-x)=f(x) and odd if  f(-x)=-f(x).

Solution
a) Odd  \sin(-x)=-\sin(x)
sin(x)
b) Even  \cos(-x)=\cos(x)

sin(x)
c) Odd  \sin(-x)\cos(-x)=-\sin(x)\cos(x)

sin(x)
d) Even  (-x) \sin(-x)=(-x) (- \sin(x))=x \sin(x)
sin(x)

e) Even  (-x)^2=x^2
sin(x)
f) Neither  \sin(-x) + \cos(-x)= -\sin(x) + \cos(x)

sin(x)

Published by Yaz

Hi! Yaz is here. I am passionate about learning and teaching. I try to explain every detail simultaneously with examples to ensure that students will remember them later too.

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1 Comment

  1. Please can you solve this example
    X(t)=u(t-1)-u(t-3)
    Express the signal using its even function xe(t) and Odd function xo(t)
    Then sketch the original signal

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