Some of the questions that I am asked by Pre-Calculus students usually go something like:
What is this thing about “Pi” [p]?
Why do we have to do measurements in radians, and What are Radians anyway?
The answer to these and other questions like them rest in understanding the
The Unit Circle is designed to show that there is a changing relationship between the x and y
So Why “Pi” [p]?
This is answered by looking at the formula for the Circumference (distance around the circle). We know that Circumference (C) is equal to two times pi times the radius. Or in math terms:
C = 2pr
Since all the way around a circle is 360o;
360o = 2pr
Dividing both sides by 2, you are going only half way around the circle so:
180o = pr
And because r = 1
180o = p
So the basic formula for all circles is that “Pi” [p] is 180o. Since this is based on the radius the measure is called Radians!