Cyclical Functions

crest

highest point of a wave

a

represents amplitude

b

represents frequency

c

represents phase shift

d

represents vertical translation

amplitude

the distance between the sinusoidal axis and the maximum and the axis and the minimum

frequency

the distance from the beginning of a cycle to the start of the next

phase shift

the horizontal shift of the sine graph, left or right, from the parent graph

maximum value

the largest value in a set of data d + a

trough

the lowest point of a wave

vertical translation

the shift of the sine graph up or down from the parent graph

minimum value

the smallest value in a set of data d - a

Factor y = 24 sin (.03x + 0.42) - 200

y = 24 sin [.03(x + 14)] - 200

Factor y = 24 sin (.03x + 14) - 200

y = 24 sin [.03(x + 466.7)] - 200

Factor y = 24 sin (.03x - 0.42) - 200

y = 24 sin [.03(x - 14)] - 200

Factor y = 24 sin (.03x - 14) - 200

y = 24 sin [.03(x - 466.7)] - 200

Frequency of y = 42 sin (0.15x - 56) + 39

0.15

Phase shift of y = 42 sin (0.15x - 56) + 39

373.33

Vertical translation of y = 42 sin (0.15x - 56) +39

39

Amplitude of y = 42 sin (0.15x - 56) + 39

42