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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
Unit 9:
Trigonometry
Recall from Geometry:
Trigonometry istherelationship
betweenthelengthsofsidesand
anglesinatriangle.
This year:
Trigonometricfunctions arebased
onthegeometryofthecircleand
rotationsarounditscenter.
Lesson #1
Rotations and Angles
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
An angle is in standard position
is when the initial side is the
positive x-axis and the vertex is
at the origin.
The ray on the x-axis, is called the
intial side of the angle, and the
ray at which the rotation ends is
the terminal side of the angle.
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
An angle formed by a
counterclockwise rotation has a
positive angle measure.
An angle formed by a clockwise
rotation has a
negative angle measure.
Terminal Angles w/ Quadrants
Quadrantal Angles – angle in
standard position whose terminal side
lies on one of the axes.
ex) 0°, 90°, 180°, 270°, 360°
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
Examples
Determine the quadrant in which an
angle of the given measure lies.
1. 140°
II
2. -168°
III
3. 500°
II
4. -34°
IV
Coterminal Angles
Angles in standard position having
the same terminal side.
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
If two angles are coterminal, the
difference in their measures is 360°
or a multiple of 360°
Examples: Find the angle of smallest
positive measure coterminal with an
angle of the given measure.
1. 400°
40°
2. -110°
250°
3. 790°
70°
Reference Angles
Associated with every angle drawn in the standard position
(exceptquadrantal angles)there is another angle called
the reference angle. The reference angle is the
positive acute
angle formed by the terminal side of the
given angle and the x-axis.
Reference angles may appear in all four
quadrants. Angles in quadrant I are their own
reference angles.
Remember! The reference angle is measured from the
terminal side to the x-axis. (NOT THE Y‐AXIS!)
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
Remember: The reference angle is measured
from the terminal side to the x-axis.
(NOT THE Y‐AXIS!)
Remember: The reference angle is measured
from the terminal side to the x-axis.
(NOT THE Y‐AXIS!)
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
Remember: The reference angle is measured
from the terminal side to the x-axis.
(NOT THE Y‐AXIS!)
Remember: The reference angle is measured
from the terminal side to the x-axis.
(NOT THE Y‐AXIS!)
Unit 9: Trigonometry
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Lesson #1: Rotations and Angles Algebra II with Trigonometry CC
Examples:Draweachangleinstandard
positionandidentifythereferenceangle.
2.
120°
1.
°
330°
°
Examples:Draweachangleinstandard
positionandidentifythereferenceangle.
Unit 9: Trigonometry
4.
225°
3.
°
45°
°
8