What is so special about the number $360$ anyway? Why not $100$ degrees in a circle?

It could be because the ancient Sumerians preferred to count in groups of $60$. It could be because the ancient Mayans realised that one year is approximately $360$ days, so the Earth moves $1^{\circ }$ around the Sun each day.

In our modern civilisation, we are less concerned with counting and astrology, and more concerned with having convenient mathematical formulas. Therefore, instead of degrees we use radians. As we will see in the next example, there are exactly $2\pi$ radians in a whole circle, and everything else follows from there.

1. Complete the diagram below:

2. • Convert ${100}^{\circ }$ into radians.

   • Convert $-1.5\text{rad}$ into degrees.

   • Convert $\frac{7\pi }{12}\text{rad}$ into degrees.