In This Chapter
Defining a radian
Converting degrees to radians and vice versa
Seeing situations where using radians is best
A person's first introduction to angles is usually in terms of degrees. You probably have an idea of what a 30-degree angle looks like. (If not, review Chapter 4.) And even most middle-school students know that a triangle consists of 180 degrees. But most of the scientific community uses radians to measure angles and solve trig equations. Why change to radians? Why fix what ain't broke? Read on.
A radian is much bigger than a degree. Early mathematicians decided on the size of a degree based on divisions of a full circle. A degree is the same as a slice of of a circle. No one knows for sure how the choice of 360 degrees in a circle came to be adopted. In any case, 360 is a wonderful number, because you can divide it evenly by so many other numbers: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. The early measures of time and distance relied on having convenient ...