Name: _______________________
Graphing Basic Sine and Cosine Functions with Excel (Modified with GC)
Objective: Analyze the graph of y = sin x and y = cos x
Using the Excel Spreadsheet on my website, answer the following questions:
Use your spreadsheet and graphs to answer the following questions about the sine and cosine graphs.
1.
How are the graphs of y = sin x and y = cos x similar?
2.
How are the graphs of y = sin x and y = cos x different?
3.
Which angles, in radians, have the maximum sine value?
4.
Which angles, in radians, have the minimum sine value?
5.
Which angles, in radians have a sine ratio of 0?
6.
Which angles, in radians, have the maximum cosine value?
7.
Which angles, in radians, have the minimum cosine value?
8.
Which angles, in radians have a cosine ratio of 0?
9.
Which angles, in radians, have the same sine and cosine ratios?
10.
Can you think of a way to use your spreadsheet to verify that sin2 x + cos2 x = 1
11.
If you were going to sketch a graph of the sine function and the cosine function, what key
points on the graph would you keep in mind?
Use your GRAPHING CALCULATOR to graph each of the following:
1. Put your calculator in RADIAN mode.
2. Change your window to:
x-min= - /2
x-max = 4
x-scale = /2
y-min = -5
y-max = 5
y-scl = 1
Example 1:
y = 1sin x
y = 2 sin x
y = 5 sin x
y = -3sin x
y=
1
sin x
2
How does the coefficient in front of the sine function
affect the shape of the graph?
How does a negative coefficient affect the graph?
What is the equation of the graph at right?
________________________________________________
Example 2:
y = sin x
y = sin x + 1
y = sin x + 3
y = sin x - 4
How does a number added or subtracted from the
sine function affect the shape of the graph?
What is the equation of the graph at right?
__________________________________________________
Example 3:
y = sin x
y = sin 2x
y = sin 6x
How does the coefficient on the angle affect the
shape of the graph?
What is the equation of the graph at right?
__________________________________________________
Example 4:
y = sin x
æ xö
y = sin ç ÷
è 2ø
æ xö
y = sin ç ÷
è 5ø
How does the coefficient on the angle affect the shape of the graph?
Example 5:
Graph y = cos x.
a.) How does this graph differ from the graph of y = sin x?
b.) Using the results from the previous examples, predict what each of the following graphs will look
like compared to the graph of y = cos x.
y = 3cos x
1
y = - cos x
2
y = 2 cos 3x
y = 3cos
x
2