Transcript Trigonometry

Trigonometry
Lucas Whirley
What is trigonometry?
 Trigonometry is a type of math that deals with sides and
angles of plane or spherical triangles and the relations or
calculations associated with them.
Where/When did trigonometry
originate?
 The first known table of chords was written by Hipparchus in
Greece around 140 BC. Even though that table didn’t
survive, it is known that he wrote twelve tables of chords.
Therefore, Hipparchus is the creator of Trigonometry.
Is one mathematician responsible
for the discovery of trigonometry?
 No, even though Hipparchus was the founder he was not the
main contributor. After Hipparchus, Menelaus was the next
Greek to produce chord tables. Like Hipparchus, Menelaus’s
tables were lost. However, his work on spherics survived and
is the earliest known work about spherical trigonometry.
Ptyolemy was next and was known for splitting the 360
degree circle into 120 different parts.
Real world Trigonometry
applications
 Astronomy- today trigonometry is used to help scientists
determine how far away a star is from earth
 Navigation- trig is used by pilots because they need to
determine the angle for landing
 Music industry- believe it or not musicians that create music
on a computer program use trig. Sound engineers have to
use basic sine and cosine functions to determine which note
their using and what note their tuing
 Architecture- trig and architecture are hard to separate. Trig
is used to help determine heights of buildings and is also
useful in designing a building.
Trig functions
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Three most used:
Sine: x= o/h
Cosine: x= a/h
Tangent: x= 0/h
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Remaining three trig functions:
Secant: x= h/a
Cosecant: x= h/o
Cotangent: x= a/o
 The six functions are very similar name wise. The ratios are also related
because some of the equations are inverses of each other.
 Sine, Cosine, and Tangent were used in geometry.
Possible helpful website
 http://www.trigonometry-help.net/ seems pretty helpful,
seeing as how the URL says it all. Plus, if you get frustrated
in the future there are also some jokes.
Future Project?
 http://ime.math.arizona.edu/gteams/Profiles/VP/MusicandTrig.pdf
 In this project students will answer the question: Why does
auto tune sound so bad?
 There is a lot of freedom in how students can change this
project around to suit their needs.
Unit Circle
 The Unit Circle is a circle in which the radius is 1. The unit
circle is commonly used to understand the sines, cosines,
and tangents of angles within a circle. Yes circles and
triangles are related because circles can be subdivided into
different triangles
Works Cited
 http://dictionary.reference.com/browse/trigonometry
 http://www-history.mcs.stand.ac.uk/history/HistTopics/Trigonometric_functions.html
 http://www.ehow.com/list_7769833_real-life-applicationstrigonometry.html
 http://www.mathopenref.com/trigfunctions.html
 http://www.trigonometry-help.net/basictrigonometry.php
 http://ime.math.arizona.edu/gteams/Profiles/VP/MusicandTrig.pdf
 http://www.snow.edu/jonathanb/Courses/Math1060/unit_circ_trig
.html