The unit circle, part 1 -- what is pi?
(Re-)learn trigonometry with the unit circle.
People have different learning styles. If like me, you enjoy visual learning, the unit circle will make (re-)learning trigonometry fun.
The unit circle. A circle is defined by a center and a radius. A unit circle is a circle with a radius of 1. The unit circle is the circle with radius 1 and with its center at the origin (0, 0).
What is an angle? Pick two lines that meet at some point. What is the angle between the lines? First, draw a circle of radius one (a unit circle) with its center at the point where the two lines meet. Then imagine laying a string along the circle, joining the two points where each line intersects the circle. The angle is the length of the arc (string). Angles are arc lengths (on the unit circle).
What is pi? Draw a circle of radius one unit, say one foot, and lay a string along the circle between two points opposite each other, i.e. 180 degrees apart. The length of this string will be pi (3.14) feet, or 3 feet 1.68 inches. Pi is the arc length between two opposite points on the unit circle.
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