Download Name - Mrs. Belcher

Name:_______________________
Class Period:__________________
Gifted/Accelerated Math 3
Adapted from Acc Math 3 State Task Unit 4
Getting Started with Trigonometry and the Unit Circle Learning Task:
Before you get started, answer these few questions:
1. How many degrees are in a circle? ______
2. Can you label the four quadrants of a circle?
Do so on the graph to the right.



An angle is in standard position when
the vertex is at the origin and the initial side
lies on the positive side of the x-axis.
The ray that forms the initial side of the
angle is rotated around the origin with the
resulting ray being called the terminal
side of the angle.
terminal side
counterclockwise
130
initial side
clockwise
-230
An angle is positive when the location of
the terminal side results from a
counterclockwise rotation. An angle is
negative when the location of the terminal
side results from a clockwise rotation.
The two angles above are called coterminal because they are in standard position and share the
same terminal side. Angles are also coterminal when they share terminal sides as the result of
complete rotations. For example, 20 degree and 380 degree angles in standard position are
coterminal.
Coterminal angles Ac to angle A may be obtained by adding or subtracting n*360 degrees.
Hence: Ac = A + n*360o .
1. Measure each of the angles below using a protractor. Determine three coterminal angles for each
of the angles.
a.
b.
c.
Reference angles are the angle formed between the terminal side of an angle in standard position
and the closest side of the x-axis. All reference angles measure between 0o and 90o.
Quadrant I
reference angle
Quadrant II
Quadrant III
Quadrant IV
reference angle
reference angle
reference angle
2. Determine the reference angle for each of the following positive angles.
a. 300o
b. 135o
c. 30o
d. 210o
e. 585o
f. 870o
3. Determine the reference angle for each of the following negative angles.
a. -45o
d. -405o
o
b. -120
e. -330o
c. -240o
f. -1935o
Two positive angles  and  are
complementary (complements of each
other) if their sum is 90o .
Two positive angles are supplementary
(supplements of each other) if their sum is
180o .
Find the angle complementary to the given angle:
4. 12o
5. 0 o
6. 27 o
7. 73o
10. 115o
11. 171o
Find the angle supplementary to the given angle:
8. 13o
9. 90o
Name:_______________________
Class Period:__________________
Gifted/Accelerated Math 3
Adapted from Acc Math 3 State Task Unit 4
Angles as a Part of the Unit Circle
1. The circle below is called the unit
circle. Why do you believe this is so?
2. Duplicate this graph and circle on a
piece of your own graph paper. Make
the radius of your circle 10 squares
long (10 squares = 1 unit).
3. Fold in the angle bisectors of the right
angles formed at the origin. What
angles result from these folds?
4. Use a protractor to mark angles at all
multiples of 30o on the circle. Why
didn’t we use paper folding for these
angles?
5. Which of the angles from #3 have reference angles of 30o?
6. Which of the angles from #3 have reference angles of 60o?
7. What is the angle measure when the terminal side of the angle lies on the negative side of the xaxis?
8. What is the angle measure when the terminal side of the angle lies on the negative side of the yaxis?
9. What is the angle measure when the terminal side of the angle lies on the positive side of the yaxis?
10. For what angle measures can the initial side and terminal side overlap?