The period is the distance until the y-values repeat their cycle.

y = sin x and y = cos x have a period of 2 6.28... = 360°

A constant times the angle x changes the periods.

y = A sin Bx and y = A cos Bx have a period .

To sketch this, mark off the amplitude on the y-axis and mark off the period, , on the x-axis. Divide the period into quarters.

Example 1

y = 3 sin 5x
amplitude = |3| = 3
period =

Example 2

y = 4 cos /2 or y = 4 cos
amplitude = |4| = 4
period = = 4

Example 3

y = - sin 4x
amplitude = |-1| = 1
period =