Math 3
5-6 Graphs of Two Mystery Functions
Name_________________________
Today we will be using uncooked pasta to create the graphs of two mystery functions. What the
functions are is not important at this point, we just want to see what the graphs of these two mystery
functions look like. Carefully follow the below procedures (which will also be demonstrated) in order to
use the pasta to make graphs of the two functions. You will need tape/glue, scissors, a pencil, numerous
pretzel sticks, and accurate measurements. When we are done, we will decorate our classroom.
Shown below is what is called a unit circle. It is called a unit circle because its radius is considered 1
unit. What the unit is (inches, feet, centimeters, meters, etc.) is not important. What is important is that
the radius is 1 unit.
90
120
60
45
135
150
30
180
0
210
330
225
240
300
315
270
We are going to use this unit circle in order to make graphs of our two mystery functions. The
procedure for making each graph, along an axes to make each graph, is given on the following pages.
Be sure to carefully follow the directions!
Mystery Graph #1
1.
Using the unit circle on page one of this packet, place pretzel so that one end is at the point on
the circle indicated by the 30 degree angle on the unit circle and the pasta is perpendicular to
the x-axis.
2.
Break off the pasta so that its length is the vertical distance (perpendicularly) from the x-axis to
the point indicated by the 30 degree angle. So after you break the pretzel, the pretzel should be
perpendicular to the x-axis, with the top of the pretzel at the point labeled 30 degrees, and the
bottom on the x-axis. CHECK WITH MR. SHEPPARD BEFORE MOVING ON TO THE
NEXT STEP!
3.
On the graph at the end of this packet (titled “Mystery Graph #1), place the broken pretzel so that
one end is on the x-axis where the 30 degree angle is indicated and the pretzel is perpendicular to
the x-axis. If the angle used to find the pretzel length is above the x-axis on the unit circle, put the
pasta above the x-axis (going up) on the graph. If the angle used is below the x-axis on the unit
circle, put the pasta below the x-axis (going down) on the graph. CHECK WITH MR.
SHEPPARD BEFORE MOVING ON TO THE NEXT STEP!
4.
Tape/glue the pretzel to the sheet.
5.
Repeat steps 1 – 4 for each angle indicated on the circle.
6.
Draw a dot at the end of each pretzel to show the height of mystery function #1. Connect the
dots using a smooth curve. You have now sketched one cycle of mystery graph #1.
Questions to answer:
1.
If you continued the graph after 360 degrees, what would the graph look like? How do you
know? Refer to the unit circle in your answer.
2.
If you continued the graph in the negative direction, what would the graph look like? How do
you know? Refer to the unit circle in your answer.
3.
State the domain of the function.
4.
State the range of the function.
Mystery Graph #2
1.
Using the unit circle on page one of this packet, place a pretzel so that one end is at the point on
the circle indicated by the 0 degree angle on the unit circle and the pasta is perpendicular to the
y-axis.
y
2.
Break the pretzel so that its length is the horizontal distance (perpendicularly) from the -axis to
the point indicated by the 0 degree angle. CHECK WITH MR. SHEPPARD BEFORE
MOVING ON TO THE NEXT STEP!
3.
On the graph at the end of this packet (titled “Mystery Graph #2), place the pretzel so that one
end is on the x-axis where the 0 degree angle is indicated. If the angle used is to the right of the
y-axis on the unit circle, put the pasta above the x-axis (going up) on the graph. If the angle used
is to the left of the y-axis on the unit circle, put the pasta below the x-axis (going down) on the
graph. CHECK WITH MR. SHEPPARD BEFORE MOVING ON TO THE NEXT STEP!
4.
Tape/glue the pretzel to the sheet.
5.
Repeat steps 1 – 4 for each angle indicated on the circle.
6.
Draw a dot at the end of each pretzel to show the height of mystery function #1. Connect the
dots using a smooth curve. You have now sketched one cycle of mystery graph #2.
Questions to answer:
1.
If you continued the graph after 360 degrees, what would the graph look like? How do you
know? Refer to the unit circle in your answer.
2.
If you continued the graph in the negative direction, what would the graph look like? How do
you know? Refer to the unit circle in your answer.
3.
State the domain of the function.
4.
State the range of the function.
Mystery Graph #1 (each interval is 15 degrees)
Pasta Height
1
-1
45
90
135
180
Angle
225
270
315
360
Mystery Graph #2(each interval is 15 degrees)
Pasta Height
1
-1
45
90
135
180
Angle
225
270
315
360
Math 3
5-4 Graphs of Trigonometric Functions Notes
Name_______________________________
1.
Below is the graph of y  sin  x  , where the x-axis is in radians, over the interval 0, 2  .
Explain based on your knowledge of the unit circle, why the graph has the shape that it does.
2.
Below is the graph of y  cos  x  , where the x-axis is in radians, over the interval 0, 2  .
Explain based on your knowledge of the unit circle, why the graph has the shape that it does.
3.
Below is a graph of y  tan  (the x-axis is in radians)
a.
What is the relationship between sin  x  , cos  x  , and tan  x  ?
b.
What is happening at x 
c.
What is the domain of ℎ(𝜃) = tan⁡(𝜃)? __________________________.
d.
What is the range of ℎ(𝜃) = tan⁡(𝜃)? __________________________.

2
? Why?