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Algebra III Academic
6.1 Angles and Their Measures (Day 2)
Objective:
To use degrees to measure angles and become familiar with the unit circle.
Review coterminal angles and calculate reference angles.
Write angles in different forms.
Reference Angle: ____________________________________________________________________
Illustrations and How to Find Reference Angles…
Quadrant I
Quadrant II
r

r
Quadrant III

Quadrant IV

r
r
Steps for finding reference angles.
1. Given angle must be within one rotation of the circle 0    360. If the given angle is not, find a
positive coterminal angle.
2. Now, find the reference angle:
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Sketch the following angles and determine the reference angle.
a.  = 57°
b.  = 302°
c.  = 133°
d.  = 254°
e.  = -227°
f.  = -184°
g.  = 4897°
h.  = 220°
Algebra III Academic
Trigonometry: Angles and Degree Measure
Homework
Convert the following from degrees to radians or vice versa.
7) 225°
11)
2
7
8) 315°
12)
3
4
9) 150°
13) 
7
4
10) 75°
14) -65°
For each of the follow questions, find one positive and one negative coterminal angle. Then, draw the angle in
standard position and find the measure of the reference angle.
15) 87°
qc+ = _____
16) 562°
qc+ = _____
17) - 336°
qc+ = _____
18) - 45°
qc+ = _____
qc = _____
qc = _____
qc = _____
qc = _____
qr = _____
qr = _____
qr = _____
qr = _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
-
-
-
-
Sketch the following angles and determine the reference angle.
a.  = - 57°
b.  = - 77°
c.  = - 133°
d.  = - 254°
Sketch the following angles and determine the reference angle.
e.  = 227°
f.  = 184°
g.  = - 4897°
h.  = - 220°
Draw the following.
1) Positive acute angle terminating in quadrant I.
2) Positive angle terminating in quadrant III.
3) Positive angle terminating in quadrant IV.
1)
2)
3)
Draw the following.
4) Negative acute angle terminating in quadrant IV.
5) Negative angle terminating in quadrant III.
6) Negative angle terminating in quadrant I.
4)
5)
6)
Sketch the following angles. (Finding the coterminal angles may be helpful to determine the quadrant for the
angle that should be graphed).
a.  = 57°
b.  = 77°
c.  = 133°
d.  = 254°
e.  = -227°
f.  = -184°