Sine Wave Formula

Phase Shift

• Horizontal movement, calculated as negative c divided by b.

• Vertical movement, calculated as positive c divided by a.

• No movement, remains constant at zero.

• Random movement, calculated as the sum of a and b.

Period

• The distance for one full cycle, calculated as 2pi divided by the absolute value of b.

• The time taken to complete one full cycle, calculated as 2pi multiplied by the absolute value of b.

• The frequency of the wave, calculated as the inverse of the period.

• The amplitude of the wave, which is the maximum distance from the rest position.

Amplitude

• The distance from the midline to the peak or trough.

• The maximum distance from the midline to the peak or trough, given by the absolute value of a.

• The average value of a wave's height.

• The total distance covered by a wave in one cycle.

Sine Wave Graph

• A smooth, continuous curve that repeats every period.

• A jagged line that fluctuates randomly.

• A straight line that does not change direction.

• A series of peaks and valleys with no repetition.

Vertical Shift

• Moves the graph up or down, represented by d.

• Changes the graph's width, represented by w.

• Flips the graph vertically, represented by f.

• Shifts the graph left or right, represented by h.

Sine Wave Formula

• y = a sin(bx + c) + d, where: * a = Amplitude * b = Affects period * c = Phase shift * d = Vertical shift

• y = a cos(bx + c) + d, where: * a = Amplitude * b = Affects frequency * c = Phase shift * d = Vertical shift

• y = a tan(bx + c) + d, where: * a = Amplitude * b = Affects period * c = Phase shift * d = Vertical shift

• y = a sin(bx) + d, where: * a = Amplitude * b = Affects period * d = Vertical shift

Maximum and Minimum Values

• Max = d + absolute value of a, Min = d - absolute value of a.

• Max = d - absolute value of a, Min = d + absolute value of a.

• Max = d + a, Min = d - a.

• Max = d + 2a, Min = d - 2a.