Angles as Rotations.notebook
April 24, 2017
Angles as Rotations
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A
A complete rotation in the counterclockwise direction is 360 .
If an angle is formed by a clockwise rotation, it has a negative measure.
Sep 6­10:31 AM
Vocabulary:
Initial Side ­ the side of an angle where the rotation begins.
Terminal Side ­ the side of an angle where the rotation ends.
Standard Position ­ an angle's vertex is at the origin and its initial side lies on the positive x­axis.
Sep 6­10:38 AM
April 24, 2017
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Angles as Rotations.notebook
Initial
Jan 28­4:09 PM
If the terminal side of the angle falls on top of the x ­ or y ­ axis, we call this a quadrantal angle.
*The angle is 90 or a multiple of 90 (180 , 270 , ­180 , etc.).
Sep 6­10:45 AM
Angles as Rotations.notebook
April 24, 2017
An angle which terminates on an axis is
called a quadrantal angle.
900
00
1800
2700
Jan 29­5:04 PM
Draw a sketch of each of the angles below. In which quadrant does the terminal side of the angle lie?
1. 215o
2. 150o
3. ­460o
4. ­170 o
Sep 4­2:40 PM
Angles as Rotations.notebook
April 24, 2017
Draw your own quadrant angle!
I
III
II
IV
Apr 19­2:50 PM
Coterminal Angles ­ angles with the same terminal side.
*If two angles are coterminal, the difference in their measures is 360 or a multiple of 360 .*
To find coterminal angles add 360 or subtract 360 degrees.
Sep 4­2:40 PM
Angles as Rotations.notebook
April 24, 2017
There are an infinite number of angles that are coterminal with any given angle.
Find 4 angles that are coterminal with 910
Sep 2­9:45 AM
To find the smallest positive coterminal angle:
(means find an angle between 0 and 360 )
If given angle > 360 then subtract 360.
I f given angle is negative then add 360.
Sep 2­9:39 AM
Angles as Rotations.notebook
April 24, 2017
Ex: Find the angle of smallest positive measure that is coterminal with an angle of the given measure 4) 770
1) 550
2) ­100
5) ­380
3) 642
Sep 2­9:47 AM