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Radians & Degrees

Trig. Definitions using {x, y, r}

Trig. Definitions using Unit Circle

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 UNIT 7:TRIGONOMETRIC FUNCTIONS

 LESSON 1 :DEGREE AND RADIAN MEASURE DEFINED

 

Angle Measure:

 

Degree measure:††††

 

Text Box:
 

 

 

 

 

 

 


Radian measure: The radian measure of an angle at the center of a cirdle is the ratio of the arc length it cuts offto 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:

 

Text Box:  ††††††††††† ††††

 

 

 

 

 

Example 1: Conversions from radian measure to degree measure

 

 

 

††††††††††

 

 

 

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††

††††††††††††††††††††††††††††††††

 

 

†††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††† †††††††††††

 

 

 

 

Example 2: Conversions from degree measure to radian measure

 

 

Solution:

 

 

†††††††††††††††††††††††††††

 

 

 

 

 

††††††††

 

 

Example 3:

 

Solutions:

 

Text Box:

 

 

††††††††††††††††††††††

 

†††††††††† ††††††

 

 

 

††††††††††††††††††††††

 

 

Example 4: Angular Velocity

An electric motor turns at 2500 rpmís (revís per minute).Express this angular velocity in radians per second to the nearest hundredth.

Solution:

 

 

 

 

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