INTRODUCTION - GRAPHING SINE
Today you will explore the graph of Sine. You will use your graphing calculator. So we are all
looking at the same screen please set your window as follows
Xmin =-2π
Xmax = 2π
Xscl = π/4
Ymin=-6
Ymax=6
Yscl=1
Type y=sin(x) into Y1 on your calculator. Press the graph button. This is the graph of the sine
function. What do you notice? Sketch the graph below.
OBSERVATIONS
On the next page you will be asked to graph several versions of the sine graph and see how changes to
the function change the graph.
Type y=sin(x) into Y1 on your calculator. Sketch the graph below.
In Y2 type y=sin(x)-1. Sketch the new graph in a different color below.
Now clear Y2 and type y=sin(x)+2. Sketch the new graph below in a different color.
Now clear Y2 and type y=sin(x)-4. Sketch the new graph below in a different color.
How does the constant added or subtracted from the sine change the graph? Why
Type y=sin(x) into Y1 on your calculator. Sketch the graph below.


In Y2 type y  sin  x   Sketch the new graph in a different color below.

2


Now clear Y2 and type y  sin  x 

 Sketch the new graph below in a different color.
4
Now clear Y2 and type y  sin  x  2  . Sketch the new graph below in a different color.
How does the constant added or subtracted from x change the graph? Why
Type y=sin(x) into Y1 on your calculator. Sketch the graph below.
In Y2 type y=4sin(x). Sketch the new graph in a different color below.
Now clear Y2 and type y=2sin(x). Sketch the new graph below in a different color.
Now clear Y2 and type y=-3sin(x). Sketch the new graph below in a different color.
How does the factor in front of the sine function change the graph? Why
Type y=sin(x) into Y1 on your calculator. Sketch the graph below.
In Y2 type y  sin  2 x  Sketch the new graph in a different color below.
1 
 
Now clear Y2 and type y  sin  3x  . Sketch the new graph below in a different color.
Now clear Y2 and type y  sin  x  Sketch the new graph below in a different color.
2
How does the factor multiplied by the x change the graph? Why
The standard form of the sine function is _______________________________________________.
The amplitude is ________. Amplitude can be described as
And can be found when looking at the table or graph by
The length of the period is ___________. Period can be described as
And can be found when looking at the table or graph by
The phase shift is
. Phase shift can be described as
And can be found when looking at the table or graph by
The vertical shift is
graph by
. Vertical Shift can be found when looking at the table or