Even Functions - Odd Functions
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Even Functions - Odd Functions

Even And Odd Functions
Figure 7.13 shows two periodic signals (blue and red). Which of the signals is an even function and which is an odd function.

The string:
S7P2A21 (Identity - Physical Properties).
The math:
Even And Odd Functions
Pj Problem of interest is of type identity.
A function f(t) is even if f(-t) = f(t)
A function f(t) is odd if f(-t) = -f(t)
The red signal is a cosine function. So, it is expressed as:
f(t) = cosωt
So, f(-t) = cos(-ωt) = cos(0-ωt) = cos0cosωt + sin0sinωt = cosωt.
So, the cosine function (red signal) is an even function. The blue signal is a sine function. So, it is expressed as:
f(t) = sinωt
So, f(-t) = sin(-ωt) = sin(0-ωt) = sin0cosωt - cos0sinωt = -sinωt.
So, the sine function (bue signal) is an odd function.

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