Periodic Functions (Leaving Cert Mathematics): Quizzes

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Periodic Functions
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What are periodic functions?

Functions that repeat at regular intervals

For a function f(x)f(x) to be periodic with period TT, what must be true?

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

What is the period of sin⁡(x)\sin(x)?

2π2\pi

What is the period of cos⁡(x)\cos(x)?

2π2\pi

What is the period of tan⁡(x)\tan(x)?

π\pi

What is the period of f(x)=sin⁡(3x)f(x) = \sin(3x)?

2π3\frac{2\pi}{3}

What do graphs of periodic functions display?

A repeating pattern over one period

What is amplitude in a periodic function?

Maximum value from the midline

What is frequency in a periodic function?

How many cycles occur in a unit interval

Which phenomena can periodic functions model?

Sound waves, light waves, seasonal changes

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