Trigonometry By Melanie

What is trigonometry? Trigonometry is defined as “a branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of an angles”

What does this mean? Trigonometry uses the Greek words “trigon” and “metron” to make up its name Meaning “triangle” and “a measure” Trigonometry means the measuring of angles and sides of triangles

What makes trigonometry interesting? Who doesn’t like triangles!! Ever want to figure out how tall a mountain is? Want to calculate the distance to the sun? Trigonometry has got your back!

How do triangles affect my life? How else do I cut my pizza evenly?

But really… Trigonometry is used in our every day life. Its used to build our homes, our vehicles, our TV's, and almost every piece of technology we own. Trigonometry was used to help make even our music. Knowledge about sound waves has come from trigonometry equations!

Euclidean’s geometry (Don’t worry, this is relevant) Euclid was a Greek mathematician The sum of the angles in a triangle always equals to two right angles In Euclid’s geometry the three sides of a triangle add up to a straight line But this has limitations,

Hipparchus A Greek astronomer and mathematician named Hipparchus studied the movements of the Earth and the Sun to answer the problem: » Does the sun revolve around the Earth or does the Earth revolve around the Sun? Using Euclid’s geometry, Hipparchus tried to find an answer to this question but realized that Euclid’s geometry wasn’t made for the comparison of moving things Hipparchus used the Pythagorean theorem to calculate a list of sines and cosines to then be able to measure the changes in triangles

Pythagorean theorem Pythagoras wanted to prove A 2 + B 2 = C 2 Two thousand years earlier the Sumerians already knew about this equation and used it in many of their measurements but Pythagoras wanted to be sure it was always going to be true. Pythagoras stated that in any right triangle, the area of the hypotenuse square is equal to the sum of the areas of the adjacent and the opposite squares.

Think triangles are boring?

Try this! Draw a straight line on a piece of paper Draw more lines starting from the middle of your first line that are half the size of the diameter and going in any direction Keep your pencil on the paper Then make a straight line from where your pencil ended and connect it to your first line making a 90 degree angle. This will make a triangle! Do this a few times

It will look something like this!

What do you notice? If you continued to draw triangles like this until they are all side by side, it will create a circle! Many mathematicians have found that they can relate this to a repeating wave, called sine waves. These waves are commonly found in nature

Let’s wrap this up… Triangles are awesome They help build things we use We rely on triangles to cut our pizzas evenly Its fun to draw It can relate to sine waves Hipparchus is one smart cookie

Bibliography triangle.swf&w=405&h=510&col=#FFFFFF&title=Sine,+Cosine,+Tangent triangle.swf&w=405&h=510&col=#FFFFFF&title=Sine,+Cosine,+Tangent