Download A Favorite Recipe for Trigonometric Pasta - Hall-Trig-Course

A Favorite Recipe
for
Trigonometric
Pasta!
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Build the six trigonometric functions using pasta! Yes…pasta! And you will need a
paper plate. Participants will receive teacher perspectives of the activities shared in the
workshop.
 9-12
 Algebra
 Manipulative Targeted: Building models using simple materials
 Two overheads
Materials
 2 - 6 in paper plates (bigger size creates larger sinusoids)
 Linguine (flat spaghetti)
 Scotch tape
 2 sheets 12x18 of colored paper or 8.5x11 xerox paper
 Protractor
 Ruler
 Unit circle model
 Teacher models
 Template for sin, cos (paper plate folded with 16 unit circle points labeled)
 Template for csc, cot (horizontal tangent lines at 90 and 270)
 Template for tan, sec (vertical tangent lines at 0 and 180)
Why?
Students who have learned the relationships between the sides of a 45-45-90 triangle and
a 30-60-90 triangle and have labeled coordinates of the unit circle and have recited SOHCAH-TOA, may still need more concrete experiences with the 6 different trig ratios.
This activity will help students make more connections from their prior knowledge of the
unit circle and the ratios of two sides of a triangle to actually create the graphs of the six
trigonometric functions.
Procedure
Sin & Cos:
 Fold a paper plate into 6ths and 4ths. Label each crease with the 16 common
degrees found on the unit circle.
 Create and draw your axes. 6in paper plate has approximately an 18 in
circumference. Every 1.5 inches equates to 15 degrees. You will actually snap off
20 pieces of pasta. The graph looks better to include 15, 165, 195, and 345
degrees.
 Snap pasta lengths using the paper plate (aka - unit circle) as your gauge.
 Tape the pasta to set of axes drawn the long paper.
 Draw points at the end of each pasta, connect the points to make a smooth curve.
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Csc & Cot
 Make another set of axes like sine and cosine
 Start with the template for csc & cot (horizontal tangent lines at 90 and 270)
 Csc in the reciprocal of sine, so the opposite side needs to stay a constant one.
The hypotenuse extended to a horizontal tangent line will be the length of the
snapped pasta. Notice as x  90, the hyp  to 1! Also as x 0, the hyp 
infinity! There’s lots of foreshadowing opportunities.
 Cot is the reciprocal of tangent, so again the opposite side needs to stay a
constant one. Snapping pasta lengths using the adjacent side creates this graph.
Notice as x 90, adj side  0 and as x0, adj side  infinity.
Sec & Tan
 Make another set of axes like sine and cosine
 Template for tan, sec (vertical tangent lines at 0 and 180)
 Sec in the reciprocal of cosine, so the adjacent side needs to remain a constant
one. The hypotenuse extended to a vertical tangent line will be the length of the
snapped pasta. Notice as x 90, the hyp to infinity. Also as x 0, the
hypto one.
 Tan is the ratio of opposite to adjacent, to again the adjacent side need to remain a
constant one. Snapping pasta lengths using the opposite side creates this graph.
Notice as x90, adj side  to infinity and as x0, the adj side to one.
Once the graphs have been created, complete the following pages, which unite graphical,
numerical, and analysis.
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Y = sin(x)
Sketch the sine graph below.
Angle sin(x)
in
exact
degrees value
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
What is the domain for sin x?____________
What is the range for sin x?______________
As x 0 degrees, sin x  ______
As x  90 degrees, sin x  ______
As x  180 degrees, sin x  _____
As x  270 degrees, sin x  _____
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Y = cos(x)
Sketch the cosine graph below.
Angle cos(x)
in
exact
degrees value
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
What is the domain for cos x?______________
What is the range for cos x?_______________
As x 0 degrees, cos x  ______
As x  90 degrees, cos x  ______
As x  180 degrees, cos x  _____
As x  270 degrees, cos x  _____
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Y = tan(x)
Angle
in
degrees
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
sin(x)
exact
value
Sketch the tangent graph below.
cos(x)
exact
value
tan(x)
exact
value
What is the domain for tan x? _________________
What is the range for tan x? __________________
As x 0 degrees, tan x  ______
As x  90 degrees, tan x  ______
As x  180 degrees, tan x  _____
As x  270 degrees, tan x  _____
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Y = csc(x)
Sketch the cosecant graph below.
Angle sin(x) csc(x)
in
exact exact
degrees value value
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
What is the domain for csc x? _________________
What is the range for csc x? __________________
As x 0 degrees, csc x  ______
As x  90 degrees, csc x  ______
As x  180 degrees, csc x  _____
As x  270 degrees, csc  _____
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Y = sec(x)
Sketch the secant graph below.
Angle cos(x) sec(x)
in
exact exact
degrees value value
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
What is the domain for sec x? _________________
What is the range for sec x? __________________
As x 0 degrees, sec x  ______
As x  90 degrees, sec x  ______
As x  180 degrees, sec x  _____
As x  270 degrees, sec  _____
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017
Y = cot(x)
Sketch the cotangent graph below.
Angle tan(x) cot(x)
in
exact exact
degrees value value
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
What is the domain for cot x? _________________
What is the range for cot x? __________________
As x 0 degrees, cot x  ______
As x  90 degrees, cot x  ______
As x  180 degrees, cot x  _____
As x  270 degrees, cot x  _____
Created by Teresa Hall
North Pole High School
[email protected]
6/26/2017