S
ECT
. 3.3 M
EASURING
A
NGLES
IN
S
TANDARD
P
OSITION
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I) R
EVIEW
: Q
UADRANTS
& X /Y
AXIS
Center: Origin (0,0)
On the X-axis:
Right – Positive
Left - Negative
On the Y-axis:
Up – Positive
Bottom - Negative
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II) U
NIT
C
IRCLES
& R
OTATIONS
A “unit circle” is a circle rotated around the origin with a radius of 1
unit
The radius starts to rotate from the right side (
Initial Arm
)
The line rotating around the center is called a “
Terminal Arm
”
Rotated Counter clock-wise (positive angle)
Rotated Clock-wise (negative angle)
Positive
Direction
Negative
Direction
Initial Arm
Terminal Arm
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III) A
NGLES
IN
S
TANDARD
P
OSITION
:
All angles in “standard position” begin from the Initial arm
(right)
The angle is created by rotating the Terminal arm around
the origin (counter-clockwise)
in standard position
Ex: Draw the following angles in standard position:
a) 62°
b) 152 °
in standard position
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Ex: Draw the following angles in standard position:
a) 312°
b) -77°
in standard position
in standard position
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Ex: Draw the following angles in standard position:
a) 2.5
π
b) 9.42 radians
in standard
position
9.42 radians in
standard position
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IV) C
O
-
TERMINAL
A
NGLES
Angles that have their terminal arms at the same
position
Co-terminal angles have a difference of 360° or multiples
of 360° (Full circles)
ie: 30°, 390°, 750°, -330°, -330°, -690°, ..etc
All these angles have the same
Position, “Co-terminal Angles”
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Ex: Given the following angles, provide two co-terminal
angles and a formula for all the co-terminal angles
Add/subtract full circles
to get co-terminal angles
All co-terminal are sums/
differences of 360°
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V) R
EFERENCE
A
NGLES
An angle created by the
terminal arm
and
X-axis
.
Reference angles must be in the
same quadrant
as the
terminal arm
Ex: Given the following angles in standard position, find the
reference angle
in standard position
in standard position
Reference
Angle
Reference
Angle
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Ex: Given each of the following terminal arms, indicate
which is the reference angle:
NEITHER!!
NOTE: THE Reference angles must be formed with the X-axis and
it must be in the
same quadrant
as the terminal arm
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Practice: Find the reference angle for each of the following
angles in standard position:
Reference
Angle
Reference
Angle
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P
RACTICE
: F
IND
THE
REFERENCE
ANGLE
FOR
EACH
OF
THE
FOLLOWING
ANGLES
IN
STANDARD
POSITION
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H
OMEWORK
:
Pp 173 to 175 #1 – 13
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