4.2 Graphing Sine and Cosine
Period
4.1 Review
• Parent graphs f(x) = sin(x) and g(x) = cos(x)
• For y = a*sin(bx - c) + d and y = a*cos(bx - c) + d,
the sinusoidal axis is y = d and the amplitude is
|a|.
• To graph:
1)Graph SA
2)Find period 2π/b
3)Mark off each increment on xaxis period/4
4)Plot the following points
(opposite if a is neg, max = d + |a|, min = d – |a|,
start on y-axis and go 1 increment at a time):
Sin – SA, max, SA, min
Cos – Max, SA, min, SA
Period
• A function with period P will repeat on
intervals of length P, and these intervals are
referred to as periods.
• Typically, sine and cosine take 2π to repeat.
• The period can be altered.
• With a graph, you can determine period by
finding the horizontal distance between
consecutive maximums or minimums.
What are some things that are
periodic?
• Ex: Average daily temperature
Graphing Calculator Investigation
• Graph each of the following and determine
the period of the function. Then, try to figure
out how to determine period from just the
equation.
Y = sin(2x)
y = cos(4x) - 2
Y = 2sin(x/2) + 1
y = -3cos(πx/12)
Y =-4sin(πx – 1)
y = 2cos(πx/2 + 2)
Given y = a*sin(bx-c) + d or y = a*cos(bx-c) + d,
the period of the function is
2𝜋
𝑏
Even and Odd
• b must always be positive. We can use
even and odd properties to make it + if it is
not.
• Sin is _________ Cos is _________
• Use even and odd properties to make b +:
Sin(-2x)
Cos(-π/2)
Cos(-3x – π)
Sin(5 - πx/4)
Guided Practice
• Find the amplitude, period, increment, S.A.,
domain and range and graph each function:
Y = 4cos(2x) – 3
Y = -sin(x/3) + 2
Y = 2cos(3x) – 4
Y = 3sin(3x)
Y = 3cos(x/2) + 1
Y = -2sin(2x) - 2
Homework
• Find the amplitude, period, increment, S.A.,
domain and range and graph each function:
Y = 2cos4x – 1
Y = -2sin(x/4)
Y = -3cos2x +3
Y = 4sin3x
Y = -cos(x/2)
Y = 2sin4x - 2