What is the period of the sinusoidal graph?

Question

Answer 1

Hi Saja,

The period, by definition, is the length of a complete cycle. You can also look at it as the distance between two identical consecutive events.

Take your graph. There's a peak that happens when the x-value is 1. When does the next OR previous peak happen? Your graph shows the previous peak happening when the x-value is -2.

Now, find the distance between those two identical consecutive events (here, two consecutive peaks): 1 - (-2) = 3

So the period here equals 3.

Answer 2

write the equation in the form

f(x) = AsinB(x +C) + D

where A= amplitude = half the difference between max and min values

B = 2pi/period

period = 2pi/B

C=a horizontal phase shift

D = midline

Calculate B, the find the period = 2pi/B

in the given graph D = 0

A = 2

C = maybe 0.25 or so

B =2pi/3

period = 2pi/B = 3

period looks like 3

Answer 3

The period is the distance between two repeating points on the graph. The easiest places to check are at the highest or lowest points.

How far is it from (-2,2) to (1,2)?