Integrating Technology Into Instruction
Principles and Standards
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In the NCTM’s call for change, the
Standards recognized the impact that
technology tools have played on the
way mathematics is taught, by freeing
students from time-consuming,
mundane tasks and giving them the
means to see and explore interesting
relationships.
TEAM-Math Curriculum
G5. Verify simple trigonometric identities
using Pythagorean and/or reciprocal
identities.
 G6. Solve general triangles, mathematical
problems, and real-world applications using
the Law of Sins and the Law of Cosines.
 G7. Define the six trigonometric functions
using ratios of the sides of a right triangle,
coordinates on the unit circle, and the
reciprocal of other functions.
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Continued…
A1. a. Identify and graphically represent:
y=sin x, y=cos x, y=tan x
Constructing graphs by analyzing their
functions as sums, differences, or products
 b. Translate, rotate, dilate, and reflect
trigonometric functions.
 d. Determine period and amplitude of sine,
cosine, and tangent functions from graphs
or basic equations.
 e. Solve equations and inequalities
including: Trigonometric
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Alabama Course of Study
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7. Solve equations, inequalities, and applied
problems involving absolute values, radicals,
and quadratics over the complex numbers, as
well as simple trigonometric, exponential, and
logarithmic functions.
9. Graph trigonometric functions of the form
y=a sin(bx), y=a cos(bx), and y=a tan(bx).
a. Determining period and amplitude of sine,
cosine, and tangent functions from graphs or
basic equations
b. Determining specific unit circle coordinates
associated with special angles
Continued…
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10. Solve general triangles, mathematical problems,
and real-world applications using the Law of Sines
and the Law of Cosines.
a. Deriving formulas for Law of Sines and Law of
Cosines
b. Determining area of oblique triangles
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11. Define the six trigonometric functions using ratios
of the sides of a right triangle, coordinates on the unit
circle, and the reciprocal of other functions.
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12. Verify simple trigonometric identities using
Pythagorean and/or reciprocal identities.
Technology
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“Students should learn to recognize how
the values of parameters shape the
graphs of functions in a class” (NCTM).
Types of Technology
Graphing Calculator
 TI-Nspire: Interactive Classroom
 Geometer’s Sketchpad
 Smart Tools:
*Smart Board
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*Smart Slate
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www.wolframalpha.com
*Computational knowledge engine
Amplitude
Definition: The graph of y= a sin(x) or y=
a cos(x), with a ≠ 0, will have the same
shape as the graph of y= sin(x) or y=
cos(x), respectively, except with range
[-|a|, |a|]. The amplitude is |a|.
 The amplitude changes the “height” of
the graph.
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Period
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Definition: For b>0, the graph of
y=sin(bx) will resemble that y=sin(x), but
with period 2π/b. Also, the graph of y=
cos(bx) will resemble that of y=cos(x),
but with period 2π/b.

The period is the “length” of the graph.
When b changes it will affect the period.
Graphing Calculator

We are going to use the graphing
calculator to graph sin(x), cos(x), and
tan(x) functions. We will notice how
changing certain parameters affects the
period and amplitude of the graphs. The
graphing calculator will make it easy for
the students to notice how these
changes in functions affect the graphs. If
we had to do these calculations by hand
it would be very tedious for the student.
Graphing
“Students should learn to recognize how
the values of parameters shape the
graphs of functions in a class” (NCTM).
 CAS- Computer Algebra Systems
-Graphs functions and relations
-Can compute values of functions or
solutions to equations
-Carries out manipulations of symbolic
expressions
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Graphing Functions
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Y=sin(x)
Y=cos(x)
Y=tan(x)
Y=2sin(x)
Y=2cos(x)
Y=1+sin(x)
Y=1+cos(x)
Y= - cos(x)
Y= - sin(x)
Y=sin(2x)
Y=cos(2x)
For each of the
following:
1. Hit Y=
2. Type in the function
and close
parenthesis
3. Hit graph
Graphing Calculator: Cosine

Y1=cos(x)

Y2=1+cos(x)
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Y1=cos(3x)
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Y1=2cos(x)
Geometer’s Sketchpad
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Y=sin(x)
Y=2sin(x)
Y=sin(2x)
Y=1+sin(x)
Y=cos(x)
Y=2cos(x)
Y=cos(2x)
Y=1+cos(x)
Y= - cos(x)
Y=tan(x)
1. After opening GSP, go to
the toolbar and click on
graph.
2. Go to grid form and click
on rectangular
3. Next go to graph again
and click on plot new
function
4. Type in the function
5. It will ask if you want to
change your graph into
radians. Click yes so you
can see the graph
continued.
Geometer’s Sketchpad
1. After opening GSP, go
to the toolbar and click
on graph.
2. Go to grid form and
click on rectangular
3. Next go to graph again
and click on plot new
function
4. Type in the function
5. It will ask if you want
to change your graph
into radians. Click yes
so you can see the
graph continued.
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Let’s graph sin(x) first.
Changing the Coefficient
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Now let’s change
the coefficient to 2.
F(x)= 2sin(x)
If you graph the
picture on the same
as before it gives
you the chance to
see the change.
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By changing the
coefficient notice
that the graph goes
higher.
Adding a Constant

Let’s now graph f(x)=1+sin(x)
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Adding or subtracting a number to
sin(x) is going to shift the graph up or
down.
Cosine
Now let’s look at cosine.
 Graph f(x)=cos(x)
 Next graph f(x)= - cos(x) on top of
f(x)=cos(x).
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Wolframalpha.com: Tangent

Go to
www.wolframalpha.com

Type in tan(x)
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Change the function to
make it negative
- tan(x)
Illuminations
Illuminations has over 100 online
activities.
 http://illuminations.nctm.org/ActivityDetai
l.aspx?ID=174
 This activity is on graphing trig functions.
It is easy to use.
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Solving Triangles
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“In grades 9-12 all students should use
trigonometric relationships to determine
lengths and angle measures” (NCTM).

“Some Old Horse Caught Another Horse
Taking Oats Away.”
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Sinx=opposite / hypotenuse
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Cosx=adjacent / hypotenuse
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Tanx=opposite / adjacent
Geometer’s Sketchpad: Solving Triangles
Let’s use sin x to find side AB.
 * sin(x)=opposite/hypotenuse
 Sin(46.63)=AB/9.21, so AB=6.69
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Webmath.com
Solving Right Triangles
 Interactive
 Visual
 Find sides or angles
 http://www.webmath.com/rtri.html
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Youtube.com
Solving Triangles
http://www.youtube.com/watch?v=XFh_
JC7OSrg&feature=fvw
 Solving Identities
http://www.youtube.com/watch?v=9uoK
utwuCio
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In summary…
Technology is beneficial
 Makes graphing easier
 Can create triangles themselves
 Visual
 Hands on
 Fun!!!
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Technology
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“When students can see math in
different ways, they are able to broaden
their critical thinking skills and discover
meaningful real-world connections”
(Ouellette).
References
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National Council of Teachers of Mathematics (NCTM).
(2000). Principles and standards for school
mathematics. Reston, VA: Nation Council of Teachers
of Mathematics.
Ouellette, Steve. Guide to TI-Nspire Technology. Cliff
Notes. Wiley Publishing. December 3, 2009.
TEAM-Math. Retrieved December 1, 2009, from
TEAM-Math Curriculum Guide Web site: http://teammath.net/curriculum/index.htm
Illumination Activities
Webmath. Retrieved December 1, 2009, from webmath
website: http://www.webmath.com/rtri.html
Youtube Videos