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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].
Relation between Radians and
degrees:
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:
