Even and Odd Functions
Strings (SiPjAjk) = S7P2A21 Base Sequence = 12735 String Sequence = 12735 - 2 - 21
Figure 7.13 shows two periodic signals (blue and red). Which of the signals is an even function and which is an odd function.
S7P2A21 (Identity - Physical Properties).
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.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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