Chapter 6: Radians

• $\mathbf{\text{Arclength and Radians}}$
• $\mathbf{\text{Circular Functions}}$
• $$\mathbf{\text{Graphs of the Circular Functions}}$$

Have you ever wonderd why we divide the circle into 360 degrees? Nobody really knows the answer, but it may well have started around 600 BCE with the Babylonians.

The Babylonians lived between the Tigris and Euphrates rivers in present day Turkey and Syria. They kept written records using a stylus to press cuneiform, or wedge-shaped, symbols into wet clay tablets, which were then baked in the sun. Thousands of these tablets have survived and give us detailed information about the mathematical practices of the time.

The Babylonians used a base 60 number system because the number 60 has many factors. They did not invent decimal fractions, so they found it difficult to deal with remainders when doing division. But 60 can be divided evenly by 2, 3, 4, 5, and 6, which made calculations with common fractions much easier.

We still see traces of their base 60 system in our own day: there are 60 seconds in a minute, and 60 minutes in an hour.

In geometry, Babylonian mathematicians used the corner of an equilateral triangle as their basic unit of angular measure, and naturally divided that angle into 60 smaller angles. Now, if the corners of six equilateral triangles are placed together they form a complete circle, and that is why there are six times 60, or 360 degrees of arc in a circle.