TrigonometryAnna Wilson

What is Trigonometry?

• Trigonometry is the branch of mathematics that deals

with the relationships between the sides and the angles

of triangles and the calculations based on them,

particularly the trigonometric functions.

Origins

•Early trigonometry originated in Egypt as early as 13th century B.C.

•Was used to calculate the height of objects using shadows

History of Mathematics; Advanced Mathematical Concepts Textbook

Who is responsible?

•There are multiple contributors to the foundation of trigonometry as we know it today.

•Hipparchus, Menelaus, Ptolemy were three major founders of trigonometry

Hipparchus• Hipparchus is “credited with the foundation of

trigonometry”

• Believed to have produced a “12 book treatise on the construction of a table of chords”

History of Mathematics; Advanced Mathematical Concepts Textbook

Menelaus• In about 100 A.D. he was “credited with the first work on

spherical trigonometry”

• Also “wrote a treatise on chords in a circle”

History of Mathematics; Advanced Mathematical Concepts Textbook

Ptolemy• Produced another book of chords believed to have been

“adapted from Hipparchus’s treatise”

History of Mathematics; Advanced Mathematical Concepts Textbook

Applications

•Surveyors use trigonometry to figure out the distance across rivers by using the tangent function

Application 2

•Trigonometry is often used to determine the height of towers and mountains

Application 3

•Trigonometry is used in oceanography when calculating the heights of tides in the ocean

Application 4

•Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles

Functions, Functions, and More Functions• The three main functions

are sine, cosine, and tangent

• The other three are cosecant, secant, and cotangent

• The three less used functions are the reciprocals of the ratios of the main functions

http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm

Website

•A good website to visit is http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm

•It was very helpful and had informative figures and descriptions

Owner of Echo Enterprises•Has engineering degree from Virginia Tech•Builds and designs blueprints for residential

buildings•Owner and designer of soon to be 1st

shopping center in Cumberland called Patriot Ridge

•Uses Trig ratios to help with constructionContact Information:Address: 1875 Anderson Highway, Cumberland VA 23040Telephone: (804) 492-4852

Unit Circle• A unit circle is a circle

with a radius of one whose center is at the origin of a rectangular unit system

• It can be used to find functions like sine and cosine in a triangle

• Because of this, triangles and circle are related

Advanced Mathematical Concepts Textbook