History and Uses of Trigonometry

Date: 9/10/95 at 23:33:22
From: "PHILLIP PIETRUSCHKA"
Subject:       Re: maths

What is trigonometry?

Date: 9/15/95 at 9:7:7
From: Doctor Eric
Subject: Re: maths

I asked a high school trigonometry teacher that I know to answer this one for 
me, and here's what he had to say:

Trigonometry 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.

Today, trigonometry is introduced to students as a method for finding the 
missing parts of right triangles.  In this form it is used by surveyors, 
architects and engineers, as well as navigators and astronomers.  So, it 
is pretty important.

The second level of trigonometry for today's students is circular trig.  
Students learn to see the sine, cosine and tangent ratios as they change 
as the size of the reference angles changes.  This graphs out as a wave 
shaped curve (sine wave) and can be used to represent sound, light, radio 
and many other wave forms, so scientist and engineers have found 
extensive uses for circular trig.

Trig 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.

The word trigonemetry 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 Baylonians and Greeks used trig to do astronomy.  

Trig 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?

So, stick toothpicks in Grapefruit, learn some trig, and find out how far 
they are apart.  Wow.  This could lead you into getting interested in 
hyperbolic trig, where the hyperbola x^2-y^2=1 is used instead of the 
unit circle to generate functions.  

Can you guess why spherical trig was developed before plane trig?

- Doctor Eric,  The Geometry Forum