AP Precalculus: Periodic Functions Glossary

The maximum displacement from the midline of a sinusoidal function. Amplitude = |A| in y = A sin(Bx) + D.

The coefficient B in y = sin(Bx), which controls how quickly the function completes its cycle. Related to period by B = 2π/T.

The number of complete cycles per unit of the independent variable. Frequency = 1/period = |B|/(2π).

The horizontal line about which a sinusoidal function oscillates, located at the average of the maximum and minimum values.

The smallest positive value T such that f(x + T) = f(x). For y = sin(Bx), the period is 2π/|B|.

A function that repeats its values at regular intervals. f(x + T) = f(x) for all x, where T is the period.

A horizontal translation of a periodic function. In y = sin(B(x - C)), the graph shifts C units to the right.

A transformation that flips the graph across the midline (for negative amplitude) or across the y-axis (for negative B inside the function).

A function that can be written in the form y = A sin(B(x - C)) + D or y = A cos(B(x - C)) + D, producing smooth wave patterns.

A transformation that moves the entire graph up or down. In y = A sin(Bx) + D, the vertical shift is D units.