Transcript 6.1 Angle Measure

Angle Measure
Lesson 6.1

Angle Terminology
– Initial side
– Terminal side
– Vertex
– Standard position
2

Angle Terminology
– Positive Angle
• Counterclockwise
– Negative Angle
• Clockwise
– Show positive/negative angles
3

Angle Terminology
– Coterminal
• Share the same terminal side
• Math Open Reference - Coterminal angles
4
Radian Measure

To talk about trigonometric functions, it is
helpful to move to a different system of angle
measure, called radian measure.
 A radian is the measure of a central angle
whose intercepted arc is equal in length to
the radius of the circle.
Check out “What is a Radian?”
Also, for radian measure, does circle’s size
matter?
5
How many radians in a circle?

There are 2 radians in a full rotation -- once
around the circle
 There are also 360° in a full rotation
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Radian Measure
There are 2 radians in a full rotation -once around the circle
 There are also 360° in a full rotation
 To convert from degrees to radians or
radians to degrees, use this conversion
factor:

 radians
180
180
or
 radians
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Sample Problems

Find the degree equivalent
of 3 radians:
Find the radian measure
equivalent of 210° :
4
3
4
 180 
  rad   135


  rad  7 

rad
210 

6
 180 
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
Radian – Degree comparisons
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Uses of Radian Measure

Length of an intercepted arc:
s = r
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Uses of Radian Measure

Area of a sector:
A = ½ r2 
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Angular velocity vs. Linear Velocity
– All skaters are moving at the same angular
speed
– All skaters are not moving at the same linear
speed
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Linear and Angular Speed

Linear speed is linear units / time:
s
v
t

Angular speed is radians / time:


t
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
Angle Terminology
– Coterminal
• Share the same terminal side
14