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Grade 11 Math Lab: Transcendence & Limits FREE
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Periodic Functions & Transformations
Learning Objectives
- Identify period and amplitude
- Transform trig functions
- Model real-world cycles
Key Concepts
Period
Smallest interval for one complete cycle
Frequency
Number of cycles per unit: f = 1/period
Theory
**y = A·sin(B(x - C)) + D or y = A·cos(B(x - C)) + D**
- |A| = Amplitude
- Period = 2π/|B|
- C = Phase shift (horizontal)
- D = Vertical shift (midline)
**Modeling:** Daylight hours, tides, temperature cycles, sound waves.
**Frequency:** f = |B|/(2π) cycles per unit
Examples
y = 3sin(πx/2). Find amplitude and period.
Solution: Amplitude = 3, Period = 2π/(π/2) = 4