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UNIT 7  :  TRIGONOMETRIC FUNCTIONS

LESSON 1 :  DEGREE AND RADIAN MEASURE DEFINED

Angle Measure:

Degree measure:

Radian measure: The radian measure of an angle at the center of a cirdle is the ratio of the arc length it cuts off  to the radius of the circle.

The radian measure of an angle is given by the following formula:

One radian is the measure of an angle at the center of a circle whose arc length [a] is equal to the radius [r].

In the diagram below, the arc length a equals the radius r, yielding an angle with measure of 1 radian [approx. 57.30].

Example 1: Conversions from radian measure to degree measure

Example 2: Conversions from degree measure to radian measure

Solution:

Example 3:

Solutions:

Example 4: Angular Velocity

An electric motor turns at 2500 rpm’s (rev’s per minute).  Express this angular velocity in radians per second to the nearest hundredth.

Solution: