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Radian Measure of Angles - Concept

Teacher/Instructor Norm Prokup
Norm Prokup

Cornell University
PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

An angle is the figure formed by two rays with a common endpoint. We typically use degree measures when measuring angles, however we can use radian angle measure as an alternate way of measuring angles in advanced math courses. This measure is based on using a point on the vertex and measuring the arc length compared to the radius.

I want to talk about radian measure of angles. Recall that an angle is the figure formed by 2 rays with a common end point. I've drawn 2 rays here, ray ba and ray bc and they share end point b and this figure is called an angle. Now you may remember from Geometry that degree measure is how we normally measure angles in the real world 360 degrees is one revolution of the circle that definition results in the following definitions for acute angle, right angle and obtuse angle. And acute angle is an angle between 0 degrees and 90 degrees, a right angle is an angle with a measure of exactly 90 degrees and an obtuse angle is an angle between 90 degrees and 180 degrees.
I want to talk about radian measure though, this is the way you'll see angles measured in a lot of advanced Math courses and it's based on the idea of inscribing the angle in a circle putting point b the vertex of the angle right on the center of a circle. Now here's our angle theta and this length bc or ba is the radius of the circle. Arc ac has length s we define the radian measure of an angle as theta equals s over r. The arc length divided by the radius, this is very important because in most of advance Mathematics when you do trigonometry you do it assuming the angles are in radian measure.

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