Trigonometry Project
BY: JERRY STIEG
What is Trigonometry?
 The word trigonometry comes from Greek words
meaning “the measurement of triangles”
 It is “the study of angles and of the angular
relationships of planar and three-dimensional
figures” (Weisstein)

Weisstein, Eric W. "Trigonometry." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/Trigonometry.html
When/Where did Trigonometry originate?
 Trigonometry is thought to have originated in
Greece, with ideas from Arabia and India
 It was created by astronomers and mathematicians
trying to calculate the distance of surrounding stars
and planets
 Origins do not necessarily lie with plane triangles.
How Many Mathematicians Were Responsible?
 Trigonometry is not something that was simply stumbled





upon
It took many years and different minds to advance it.
Hipparchus- Greek Mathematician- Gave a method for
solving spherical triangles
Menelaus- Also a Greek Mathematician- Expanded on
Hipparchus’s ideas and developed “Menelaus’s Theorem”
Ptolemy- “relied on Babylonian observations and
traditions”(Smoller)- one of the most influential
Mathematicians of his time.
Smoller, Laura. "The Birth of Trigonometry." The Birth of Trigonometry. UALR, May 2001. Web. 30 Aug. 2012. <http://ualr.edu/lasmoller/trig.html>.
How Many Mathematicians Were Responsible?
Hipparchus
Ptolemy
Examples of Trigonometry
 In order to fly over a mountain, you must know how tall the mountain is.
Trigonometry can be used to calculate how tall a mountain is so that
today’s airplanes can fly over them at a safe elevation. In order to calculate
this you would place yourself a certain distance away from the mountain
and then measure the angle to the top of the mountain. You then would use
the tangent Trig function. This would allow you to calculate the height of
the mountain which is opposite of the angle you know and adjacent to the
distance you know.
 In much the same way, astronomers use Trig to calculate the distance of
stars and other objects in astronomy. By knowing the distance to the moon
astronomers can use it to calculate to position of most extraterrestrial
objects.
 Sound engineers often use Trig because a computer does not usually
recognize sounds like a human, but in a mathematical way. They often use
the sine and cosine functions to calculate the sound waves.
 Trigonometry is also used in architecture. It takes the guessing out of
construction by allowing builders to calculate side with the information
given to them.
What Are the Three Most Common Trig
Functions?
 The three most popular
 There are three other less
Trig functions are:
 Sine (sin):
common trig functions:
 Cosecant Function (csc):

Opposite/Hypotenuse
 Cosine (cos):

Adjacent/Hypotenuse
 Tangent (tan):

Opposite/Adjacent

Hypotenuse/Opposite
 Secant Function (sec):

Hypotenuse/Adjacent
 Cotangent Function (cot):

Adjacent/Opposite
Are These Six
Functions
Related?
The extra three are
simply the reciprocals
of the original three
functions.
The only place I have
ever seen these
functions outside of
this research was is
geometry class when we
were studying triangles.
What is a Unit Circle?
 “A unit circle is a circle
where the radius is 1 (one
unit). The unit circle
equation is x² + y² = 1”
 This is used in cooperation
with triangles by dividing it
into pieces.
 It is helpful in figuring out
functions

Bee, Johnathan. "Unit Circle Trigonometry." Unit Circle
Trigonometry. N.p., n.d. Web. 31 Aug. 2012.
<http://www.snow.edu/jonathanb/Courses/Math1060/unit_ci
rc_trig.html>
Trigonometric Career Example
 I often use a basic form of
Trigonometry myself in my job as a
woodsman.
 Since we use a select cut technique,
we have to pick and choose what
trees we fall
 I do this by using a Biltmore stick.
This stick is to be used by stepping
sixty-six feet away from a tree and
using the stick as a visual reference
to how many 16 foot logs can be cut
from the tree, without actually
putting the tree on the ground.
This is much like measuring the
mountains in my former examples.
 The product of this work is to allow
me to know how many board feet
are in a log and whether it is worth
the time to cut it.
Link
 http://www.youtube.com/watch?v=t2uPYYLH4Zo is
an informative, but extremely goofy video. It covers
the basics of what I remember of Trigonometry from
Geometry class.
Works Cited
Bee, Johnathan. "Unit Circle Trigonometry." Unit Circle Trigonometry. N.p., n.d. Web. 31 Aug. 2012.
<http://www.snow.edu/jonathanb/Courses/Math1060/unit_circ_trig.html>.
Hayes, Malcolm E. "Welcome to Trigonometry." Welcome to Trigonometry. University of Missouri, 2002.
Web. 30 Aug. 2012. <http://braintrax.mst.edu/math/trig/trig_content/trigwelcome.htm>.
Pierce, Brandon. "What Are Some Applications of Trigonometry?" EHow. Demand Media, 10 Aug. 2011.
Web. 31 Aug. 2012. <http://www.ehow.com/info_10052141_applications-trigonometry.html>.
Roberts, Donna. "The Six Trigonometric Functions and Reciprocals." The Six Trigonometric Functions
and Reciprocals. Oswego City School District Regents Exam Prep Center, 2012. Web. 31 Aug. 2012.
<http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm>.
Smoller, Laura. "The Birth of Trigonometry." The Birth of Trigonometry. UALR, May 2001. Web. 30 Aug.
2012. <http://ualr.edu/lasmoller/trig.html>.
Weisstein, Eric W. "Trigonometry." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/Trigonometry.html