Page 243
Coterminal Angles
 Two angles in standard position that
share the same terminal side.
 Since angles differing in radian measure
by multiples of 2p, and angles differing in
degree measure by 360° are equivalent,
every angle has infinitely many
coterminal angles.
Coterminal Angles
52°
Use multiples of 360°
to find positive
coterminal angles.
p/3 radians
Use multiples of 2p
to find positive coterminal angles
Find one positive and one negative angle that
are coterminal with an angle having a measure
of 7p/4.
7p 2p
+
= 15p
4
4
7p - 2p
p
=
4
4
Find all angles that coterminal with a 60° angle.
 Since all angles that are multiples of 360°
are coterminal with a given angle, all
angles coterminal with a 60° are
represented by:
60° + 360k°
where k is an integer.
Reference Angles
 A reference angle is defined as the acute
angle formed by the terminal side o the
given angle and the x-axis.
reference angle
218°
57°
38°
128°
52°
reference angle
331°
reference angle
29°
reference angle
Find the measure of the reference angle
for each angle.
This angle is in Quadrant - 13p 2p - 5p
=
III so we must find the
3
3
difference between it
6p - 5p p
and the x-axis.
=
This angle is
3
3
3
5p - p =
coterminal with
4
5p/3 in quadrant IV, so we reference angle
5p - 4p
p
Must find the
=
4
4
4
difference between it and the
reference angle X-axis.
5p
4
Find the measure of the reference
angle for 510°
 510° is coterminal with 150°, which is in
quadrant III, so we must find the
difference between 150° and the x-axis.
 180° - 150° = 30°
reference angle
Assignment
 page 245-246
– # 24 – 62, 66, 67