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Unit 5 Day 3: Rotation Angles
Angles in Standard Position
Consider the Cartesian Plane. We consider angles to be in standard
position if their initial arm lies along the positive x-axis and their
vertex is at the origin. An angle of rotation is an angle created when
a line segment is rotates about its vertex to a terminal position.
Draw the following angles in standard position.
a) 135o
b) -60o
c) 270o
d) 490o
Coterminal Angles
Coterminal angles are angles that share the same terminal angle.
These angles differ by multiples of 360o. Moving the terminal arm
counter clockwise produces angles with positive measure while
moving the terminal arm clockwise about the origin produces
angles with negative measure.
Name two different (one positive and one negative) coterminal
angles for the previous angles.
a) 135o
b) -60o
c) 270o
d) 490o
Special Angles – Multiples of 90
Angles that are multiples of 90 are examples of rotation angles.
To determine the trigonometric
ratios of 0o, 90o and other
multiples of 90o we consider
the ratios as  decreases or
increases.

As
 decreases to approach 0o:
As
 increases to approach 90o:
As
 increases to approach 180o:
As
 increases to approach 270o:




Principal Angles
A principal angle is the smallest positive coterminal angle.
1. Determine the principal angle for:
a) -45o
b) -120o
c) 630o
2. Determine an expression for the measure of all angles coterminal
with 145o.
Homework: Pg. 213 # 1, 2ace, 3, 4acfg, 5, 6, *7