Periodic Functions (Leaving Cert Mathematics): Flashcards

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Periodic Functions
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Periodic functions

Functions that repeat their values at regular intervals

Period (TT) of a periodic function

The regular interval at which the function repeats

Mathematical condition for periodicity

f(x+T)=f(x)f(x + T) = f(x) for all xx

Period of sin(x)sin(x) and cos(x)cos(x)

2pi2pi

Period of an(x) an(x)

pipi

Amplitude in periodic functions

Maximum value from the midline

Frequency in periodic functions

How many cycles occur in a unit interval

Applications of periodic functions

Sound waves, light waves, seasonal changes

Period of f(x)=sin(3x)f(x) = sin(3x)

rac{2pi}{3}

sin(x+2pi)sin(x + 2pi) equals

sin(x)sin(x)

cos(x+2pi)cos(x + 2pi) equals

cos(x)cos(x)

Phenomena periodic functions model

Cyclic and oscillatory phenomena

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