HISTORY AND USES OF TRIGONOMETRY
 
Trigonometry (trigon = triangle) is the study of the relations between the angles and lengths of sides of triangles. At 
 
least that is the way it started back with a Greek mathematician Aristarchus of Samos (310 to 230 BC). He was 
 
interested in the movement of the earth, moon and sun. He actually compared the sine ratio of an angle (Side 
 
Opposite divided by Hypotenuse) to the size of the angle itself as an entity in itself rather than just a collection of 
 
values as you might find in a trig table. This means he is one of the first to go beyond quantitative analysis and into 
 
qualitative properties, stating that sin(alpha)/alpha is a decreasing function. 
 
 
 
By looking at the triangles made by tangents to the sun, moon and earth during eclipses, Aristarchus was able to 
 
determine the sizes of these bodies and their distances from the earth. The word trigonometry comes from the Greek 
 
and means triangle measurement. We have evidence clear back to the 13th Century BC that trig was being used. 
 
They had tables of shadow length that are just like our tangent tables. The Babylonians and Greeks used trigonometry 
 
to do astronomy. 
 
 
 
Today, trigonometry is introduced to high-school students as a method for finding the missing parts of right triangles. 
 
Trigonometry solves problems like: What is the diameter of Mars? How far is it from Seattle to Philadelphia? How 
 
much area can a windshield wiper wipe if a windshield wiper must wipe water? 
 
 
 
Trigonometry is an essential tool of The Calculus, so all students who intend to study mathematics at higher levels 
 
must include trig in their basic learning.
 
 
 
So, stick toothpicks in Grapefruit, learn some trigonometry, and find out how far they are apart. This could lead you 
 
into getting interested in hyperbolic trigonometry, where the hyperbola x2 – y2 = 1 is used instead of the unit circle to 
 
generate functions.
 
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