Graphing Sine, Cosine, and Tangent
Periodic function ­ The graph has a repeating pattern that continues indefinitely.
Cycle ­ the shortest repeating portion of a periodic function
Period ­ the horizontal length of each cycle
Amplitude ­ is 1
( M ­ m) M = maximum value of a cycle and m = minimum value of a cycle
2
Ex 1) consider the graph below of a periodic function.
a) Identify the period of the function
b) Identify the amplitude of the function.
period
Amplitude
Max = 2
Min = ­2
Title: Apr 13­7:14 AM (1 of 3)
range
.
The period ­ 1 complete cycle is a period
Look at normal sine wave in your graphing calculator
y = sin(x)
How long does it take to complete one full cycle?
2
Title: Apr 18­8:36 AM (2 of 3)
Now look at y = sin(2x)
How long does it take to complete one full cycle?
Normal Period of sine = 2
SO!
Whats the
connection?
y = sin (bx)
The period can be found by
taking the normal period and
dividing by b
Page 832 has the formula for finding period
p = 2
b
homework page 835, #'s 3, 4, 5, 8, 17, 18, 19, 21
Title: Apr 18­8:46 AM (3 of 3)