Meredith Boyajian
EDC448
Dr. Diane Kern
Text Set: Graphs of the Sine and Cosine Functions
Guiding Question:
 How are the Sine and Cosine graphs used outside of the classroom?
 What do the graphs represent?
 How does one graph Sine and cosine?
Offline Texts:
1. Hornsby, E. John., Margaret L. Lial, and Gary K. Rockswold. A Graphical Approach to
Precalculus with Limits. Boston: Pearson, Addison-Wesley, 2007. Print.
This is the text book where I had chosen to base my topic on. It is a high school leveled
Pre Calculus text. The Section is named Graphs of the Sine and Cosine Functions. It is
ten pages long including the exercises I have chosen were appropriate to be worked on. I
chose this topic because this was one of my favorite topics when I was in high school and
I hope to teach trigonometry one day at the high school level. I particularly like this
section because there are many tables and examples to help the students really understand
the material. Also the definitions are great, and the book gives an exact step by step
procedure for making a Sine or Cosine graph. The text is not difficult to understand,
especially for an eleventh or twelfth grader. Furthermore, the homework exercises are at
the perfect difficulty level for the end of this section.
2. Berger, Melvin. "Pages 1-7." The Mighty Ocean. New York: Newbridge
Communications, 1996. Print.
This is a big picture book that is sixteen pages long, but I had only chosen to use the first
seven. I had chosen to use this book because it may not be “math” related, but it explains
what waves are, why they come in different sizes and how tides are affected. The graphs
of Sine and Cosine are technically called Sine waves and Cosine waves. Tides can be
represented with the period of the Sine and Cosine waves. Furthermore, the book
explains a water cycle which is also referred to how long the period of the Sine or Cosine
wave is. Once a Sine or Cosine wave reaches its one period (x), it starts from the
beginning again at zero till it reaches that “x” period again. That is what a cycle does, just
like the tides and water cycles, as well as currents. The math term for the height of a
wave is called amplitude. The book explains the power of the heights of waves. One can
record heights of waves by using a Sine or Cosine graph. The students will be interested
with this book because they know it is way below their reading level and there are many
pictures; besides the fact that they will not be learning math at that particular moment. I
believe this is a fun way for the students to realize the representation of “nonmathematical” waves and how the background of it all is mathematics, especially Sine
and Cosine waves.
3. Berger, Melvin. The Four Seasons. New York, NY: Newbridge Educational, 2000. Print.
I had chosen another big picture book by Melvin Berger, however it has different
symbolism to the lesson. In a year there are four seasons. On the unit circle (which Sine
and Cosine are based off of) there are four quadrants. The main point of this book is to
show the cycle or period when it comes to graphing a Sine or Cosine wave. For example,
there are four seasons: Winter, Spring, Summer and Fall. In the beginning of the year we
start off with Winter, then Spring, Summer, after is Fall, and end the year while it is
Winter again. On the unit circle, we start off with 0 degrees, then 90 degrees (π/2), 180
degrees (π), 270 degrees (3π/4) and end up with 360 degrees (2π) which is the starting
point as well. Period is one of the most important aspects when it comes to graphing a
Sine or Cosine wave. It tells how long or short a cycle is. This will also grab the students’
attention because they will see a large book that one would think has nothing to do with
math and ask, “why are we reading this?” My goal is for the students to find the
symbolism of the four seasons and be able to connect it with the lesson.
Online Texts:
4. "YouTube - 3rd Rock from the Sun: Hilarious Cheer." YouTube - Broadcast Yourself. 10
Dec. 2009. Web. 12 Feb. 2011.
<http://www.youtube.com/watch?v=ulQkjvHjWEc&playnext=1&list=PL056BF612F379
7B78>.
This is just a nineteen second youtube video that is for a quick laugh about math. The
character tries to make up a cheer saying, “Sine, Cosine, Cosine Sine” followed by the
numbers of Pi. Just by this one statement it shows Sine, Cosine and Pi are all related. I
just want the students to appreciate math and joke around at the same time. I would use
this to open up the lesson to brighten up the math classroom.
5. "YouTube - Just a Unit Circle." YouTube - Broadcast Yourself. 11 Dec. 2010. Web. 12
Feb. 2011. <http://www.youtube.com/watch?v=ndVdTT1N6NE>.
Here is yet another youtube video I would like to show my students. It is 3:55 long and
three boys who make up a math song about the unit circle and graphing, to the music of
the song Just a Dream by Nelly. Using this video will hook the students because the
video is to music the students listen to, or at least heard of and it is quite Chomical to
watch. The boys in the video talk about the unit circle, which Sine and Cosine are based
off of and some Sine and Cosine graphs are shown. I do not want the students to think
they have to make up a song, but to understand why I showed the video. Instead of
reading a book or telling the students what the topic is going to be on that particular day,
it is a good approach to open the lesson. It is a quick fun way to have the students
involved and not make the lesson seem too dull.
6. "Using Sine and Cosine Functions in Real Life?" Eyes on Final Fantasy Forums. 14 Dec.
2008. Web. 13 Feb. 2011. <http://forums.eyesonff.com/help-forum/121908-using-sinecosine-functions-real-life.html>.
Here I happened to come across a blog online. It will take a student about ten minutes to
explore the whole page. Someone had posted the question, “In Pre-Calculus I have an
assignment, "To Illustrate how a sine or cosine function is applied in the real world."
Honestly, I haven't the slightest clue. Help? EDIT: Can't radio waves be graphed as
sine/cosine functions?” There are good answers and debates about this topic. I would like
the students to read this blog because it will answer the question “where are Sine and
Cosine waves used outside the classroom?” without me answering it for them. One
person explains the difference between period and frequency. This will come up in the
lesson because my goal is for the students to be able to graph a Sine or Cosine function
with the correct period. As I said before, it is one of the most important aspects when
graphing these particular periodic functions. Moreover, when I was on this site, I came
across a link that a student had posted in this response, and lead me to an article titled
How Things Work: Radio.
7. Whiston, Michael M. "How Things Work: Radio." The Tartan Online. 17 Sept. 2007.
Web. 13 Feb. 2011. <http://thetartan.org/2007/9/17/scitech/work>.
Here is the article I came across from the blog above. It should only take a student no
longer than ten-fifteen minutes to read. The text is not that difficult. I particularly like this
article because the author mentions talks about Sine waves and how it is related to radio
waves. Whiston mentions radio waves, how television uses radio waves, cell phones are
radio waves, and even astronomers use radio telescopes to direct radio waves. Amplitude
is mentioned which is an important aspect when it comes to sketching a Sine or Cosine
graph. The amplitude tells how tall or short a particular wave is. Besides the blog, this is
a really good “outside” reading to engage the students in the lesson. When I was in high
school, people would say, “I am never going to be a math teacher when will I use this
stuff?” I even say the same now when it comes to certain material. However, this article
answers this particular question. Even though one may not become a math teacher, it is
really interesting to show the students how now only math, but this particular lesson is
used outside of the classroom and in everyday life. If it weren’t for Sine waves, how
would radio waves be measured?
8. "YouTube - Pre-Calculus: Graph Sine, Cosine with Phase Shifts." YouTube - Broadcast
Yourself. 29 July 2009. Web. 16 Feb. 2011.
<http://www.youtube.com/watch?v=mC5RZVKxRNU>.
This is a 3:08 video on how to make a Sine graph. The video is easy to understand. This
material is meant for the higher grades of high school and I believe this video satisfies the
needs for the particular students in the class. I personally am a visual learner so in my
classroom I want to use my methods of learning, and apply them to my students. This
video is short long enough to grasp the students in the lesson and understand the material,
yet short enough where the students’ minds will not wonder. The man who is giving the
lesson is a little awkward so watching the video will not be as boring as listening to Ben
Stein in Ferris Bueller’s Day off. The topic of my lesson is about the periodic functions
Sine and Cosine and how to graph them. Not only does the man in the video do this, but
he talks about amplitude, phase shift and period. As previously mentioned, these are what
make each Sine and Cosine wave unique. In the classroom I would open up with this
video so the students have an understanding of what the section’s lesson is going to be
about. After they watch the video the students will have a brief understanding of the
material, and my goal is for them to apply it to the lesson. Instead of reading the section
the night before as most teachers recommend, the students can watch and listen to an
overview of the lesson, then read the text and look at it in words.
9. Stephanie. "Scribe ; Periodic Functions." Applied Math 40S. 15 May 2006. Web. 14 Feb.
2011. <http://am40s.blogspot.com/2006/05/scribe-periodic-functions.html>.
This is a blog I found online through the Wikispace. This is a blog a senior girl had
written pertaining to the lesson she had in class. The topic is about the unit circle and how
it is used for a Sine wave. She has two pictures; one of the unit circle and one of a Sine
wave. I would like my students to engage in this blog because I believe the students will
be able to relate to it more because the girl who produced this particular blog is the same
age as the students in my classroom. The lingo and understanding will be similar between
the student who wrote the blog and the student reading the blog. I would use this as an
opener with the class. After reading the blog, the students will be able to connect the
reading to the lesson. It is a quick and easy way for the students to get motive for the
lesson. Students will have questions after reading; however they will be answered when
we open the text. The lesson will be more in depth about graphing a Sine wave and its
period.
10. "Sine Waves and Sound." Demos with Positive Impact Portal. 24 May 2006. Web. 15
Feb. 2011.
<http://mathdemos.gcsu.edu/mathdemos/trigsounddemo/trigsounddemo.html>.
This webpage is great because not only does it have demos, facts, pictures and
definitions, but explain how Sine waves are used outside of the classroom. Sound is
measured by a Sine wave. The text and material is appropriate for a high school student
to understand. This is something I would have the students engage in for a whole class
period, maybe even two days. There is so much material on this page that it all cannot be
covered in just one day. This page is just like the text, only in a more friendly way.