Rekrut 1
The Unit Circle
Guiding Questions:
1. In what ways can trigonometry be of any use in the real world?
2. How is it possible that an angle measure can be constant while the sides of the angle
could extend indefinitely?
3. Is there any way that the knowledge of trigonometry can be applied to predict future
patterns?
Offline Texts:
1. Dugopolski, Mark. Fundamentals of Precalculus. Boston: Addison-Wesley, 2004. Print.
This text book contains 545 pages of mathematical content.
Although this book is considered to be a college-level textbook, I
feel it is rather easy to follow. Such a book would be helpful in a
high school classroom to prepare students for what they could
encounter as text books when they attend college in the future. In
this book the examples given are fairly easy to follow, and stepby-step solutions to the examples given highlight key points of the
problem. Aside from highlighting the key points, the examples
also explain in words what mathematical calculations are being
made. Furthermore, this text highlights in bold key definitions and contains chapter
summaries. At the end of each chapter there is a review to all of the topics that were covered.
This book contains a great deal of examples, practice problems, and odd numbered solutions
to help walk any student through understanding topics covered in pre-calculus, namely the
unit circle.
2. Sterling, Mary Jane. Trigonometry for Dummies. Hoboken, NJ: Wiley, 2005. Print.
What is interesting about this text is that it is designed to help those
individuals who do not understand trigonometry. It explains basic concepts,
examples that are easy to follow, as well as a little bit of humor. A book such
as this one could really help a student learn. Although this text is 384 pages
long, it is considered to be a “friendly book” that is easy for most students to
read. The book not only contains graphs and pictures, but also humorous
comic strips to keep the reader engaged.
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3. Sterling, Mary Jane. Trigonometry Workbook for Dummies. Hoboken, NJ: Wiley, 2005.
Print.
This workbook goes hand-in-hand with the above text. It is a workbook
that contains several problems to practice after reviewing the text. This
book is 320 pages long and contains step-by-step solutions to each
problem. What is great about both this workbook and its companion
text is that the author assumes little knowledge. For advanced
mathematics students, the practice problems would be a great review for
them. For those students who are having trouble grasping the concepts
explained in class, the book is very helpful and easy to follow.
Online Texts:
1. "Unit Circle." Math Is Fun - Maths Resources. 2011. Web. 15 Feb. 2012.
<http://www.mathsisfun.com/geometry/unit-circle.html>.
This website is perfect to present to the students at the end of the unit. It sums up all key aspects
of the unit circle including how to find radian and degree measures of the important angles.
Throughout the site are links that students can
click on for additional help. For example, if a
student forgot what a “radian” was, there is a link
that takes the student to another page that
describes radians and their relationship to degrees.
These links will be very helpful for students who
do not fully understand the mathematical
vocabulary that is being presented to them. The
step by step explanations and pictures are a great
way for students to review what they have learned
and brush up on topics they are still confused
about.
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2. "Trigonometry." The Touch Mathematics Project. Touch Mathematics, 2010. Web. 15 Feb.
2012. <http://www.touchmathematics.org/topics/trigonometry>.
This interactive webpage shows students the relationship between the unit circle and
graphing trigonometric waves. It truly displays how graphs of the trigonometric functions are
generated based on the knowledge of the unit circle. Since it is interactive, students can pick
a point on the unit circle and see where that point is located on each graph. The location of
the point is not only shown on the unit circle and the graph, but this site also displays which
quadrant the point is positioned. The fact that it is color coded and interactive is a fun and
new way for students to understand what they are learning, especially for visual and “hands
on” learners.
3. "Matheatre - Unit Circle Trigonometry - YouTube." YouTube - Broadcast
Yourself.Matheatre, 20 Dec. 2010. Web. 15 Feb. 2012.
<http://www.youtube.com/watch?v=YfcIaUF2JqM>.
This youtube video is really catchy! It explains in a song how to create the first quadrant
of the unit circle. As the song continues, the circle is being drawn according to the lyrics.
I personally enjoy the line “30, 45, 60, 90, that’s why I love unit circle trigonometry!” 30,
45, 60 and 90 represent the first four
angles of the unit circle, and these
catchy lyrics make it hard to forget that.
Auditory and visual learners could
definitely benefit from this video. Since
the topic of a unit circle is usually
taught in a pre-calculus course in high
school, I believe that this song is
cheesy enough to actually catch the
attention of students and help them
“accidentally” retain the information by
getting the song stuck in their heads.
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4. Weidner, John. "Flashcards about Unit Circle!" Study Stack. John Weidner, 2001. Web. 16
Feb. 2012. <http://www.studystack.com/flashcard-37485>.
This website has some great study tools! Besides flashcards, students can practice study
tables and matching games in order to remember the angles and coordinates on the unit
circle. What is also interesting
about this site is that students can
play hangman, complete a word
search, unscramble words or even
take a quiz to make sure the
mathematical terms and symbols
are making sense. It is important
that the students understand how
to construct the unit circle before
the knowledge of it can be
applied to solve real world
trigonometric problems.
Whether students do not
understand the vocabulary or just
simply cannot remember the coordinates of each angle, there is an option of what to study
and how to study it based on the individual wants and needs of the student.
5. Carr, Karen. "Pythagoras and the Pythagorean Theorem for Kids!" Kidipede - History for
Kids. 20 Oct. 2011. Web. 16 Feb. 2012.
<http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm>.
This article is a great introduction to the unit circle.
Since the Pythagorean Theorem can be used to find
any angle or coordinate on the unit circle, this website
will be a good refresher of how this theorem is used.
Students who claim they are “History people” and not
“Math people” could truly appreciate this site. The
article is relatively short, easy to read, and is intended
for children. For struggling readers, this article gives a
simple explanation of the Pythagorean Theorem and
includes links to vocabulary words and pictures to go
along with the descriptions. For advanced readers, this
article is meant to just refresh their memory of the
basic concepts of the theory and to see how a proof of
it can be represented pictorially. Overall, I feel that
this article can reach out to a wide range of interests,
reading levels, and learning styles.
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6. McPhee, Isaac M. "The Unit Circle: A Deceptively Simple Trigonometric Tool |
Suite101.com." Isaac M. McPhee | Suite101.com. Isaac M. McPhee, 14 Aug. 2008. Web. 16
Feb. 2012. <http://isaacmmcphee.suite101.com/the-unit-circle-a64437>.
This article is really interesting! It is a relatively short passage that explains why
knowledge of the unit circle is important
to everyday life. This would be another
great article to present to the students at
the beginning of the lesson so they
understand why they are learning the
material. This Math/Chaos Theory website
describes the importance of several topics
in mathematics such as prime numbers,
probability, percentages, etc. that are truly
interesting to read about. Students like to
read about how they can connect what
they are learning to real world
applications. This will in turn help them
make their own mental connections to
better understand and remember the
material. Upon reading this article, students will understand why they are learning the
unit circle, and they will hopefully create connections between math and the real world
that are essential to learning.
7. "Unit Circle Illustrations." The Textpotential Educational Organization. Creative Commons,
9 June 2010. Web. 16 Feb. 2012.
<http://www.textpotential.org/Textpotential/Unit_Circle_Illustrations.html>.
This website contains a series of illustrations in relation to the unit circle. Some pictures
include the unit circle being drawn as the Wheel of Fortune, a basketball, a dart board,
etc. An assignment could be give to the students asking them to draw the unit circle any
way they would like. These illustrations will help spark their creativity and display their
personalities in a mathematical drawing. These pictures that the students create could also
help them make connections between the unit circle and something that is interesting to
them. Artistic and visual learners would really appreciate this assignment. As a teacher I
would be really excited to see what pictures the students come up with.