Introduction to the
Unit Circle
Angles on the circle
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.
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.
Two angles are coterminal if 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 and 380 are coterminal because 380 = 20 + 360
1) Identify which angles ARE in standard position.
2) Determine if the angles are positive or negative. (Only those in standard position)
a.
b.
c.
d.
e.
f.
3) Sketch each of the following angles and draw a coterminal angle.
a. 30⁰
b. 100⁰
c. 220⁰ (Use a positive coterminal angle)
d. -45⁰
4) DO YOU REMEMBER? Label the quadrants on the coordinate plane.
Ordered Pairs on the Unit Circle
Warm-Up:
Which quadrant does the terminal side of the following
angles fall in?
1.
2.
3.
4.
5.
6.
7.
75⁰
351⁰
-82⁰
195.31⁰
-210⁰
750⁰
-680⁰
Why is it the “unit circle”?
What are the
coordinates of
the terminal
side for each of
the following
angles?
a. 0⁰
b. 90⁰
c. 180⁰
d. 270⁰
e. 360⁰
(0,1)
(-1,0)
(1,0)
(0,-1)
Consider 45⁰.
(0,1)
What is another
positive angle with
the same xcoordinate?
45⁰
(-1,0)
Same y-coordinate?
Negative angle with
same x?
(0,-1)
Angle greater than
360⁰ with same y?
(1,0)
Consider 30⁰.
(0,1)
What is another
positive angle with
the same xcoordinate?
30⁰
(-1,0)
Same y-coordinate?
Negative x-value?
Negative y-value?
(0,-1)
(1,0)
Lets reconsider 45⁰.
(0,1)
What are the
coordinates for the
terminal side?
(Hint: Consider a special
right triangle)
45⁰
(-1,0)
(0,-1)
(1,0)
Let’s label the unit
circle!