Warm Up
Find an angle between 0° and 360° that is
coterminal with 1190°.
Complete on your own paper and turn into the
red basket.
This circle has a radius of 1.
(0,1)
(1,0)
(-1,0)
(0,-1)
We call this
the unit
circle
because
the radius
is one unit.
Use SOH CAH TOA to figure out the coordinate of the point below, knowing that the
radius of the circle is 1.
Steps to solve:
1. Hypotenuse = radius, so your hypotenuse = 1
2. Use SohCahToa to find your x and your y (find one at a time)
(0,1)
1
(-1,0)
y
30°
x
(0,-1)
(1,0)
Answer: (.866, .5)
x: cos(30) = x / 1
x = .866
y: sin(30) = y / 1
y = .5
You Try!
Now, find the coordinates of the following
two points.
45°
x = .707
y = .707
(.707, .707)
60°
x = .5
y = .866
(.5, .866)
Now that we
know the points
for one quarter of
the Unit Circle,
we can label the
remainder of the
unit circle.
**The unit circle does
not use decimals; all
measures are in either
radians or degrees.
Here is the unit circle divided into 8 pieces. Can you
figure out how many degrees are in each division?
0,1
 2 2


 2 , 2 


 2 2


 2 , 2 


90°
135°
45°
 1,0 180°
0° 1,0
225°
 2
2


 2 , 2 


270°
0,1
315°
 2
2


 2 , 2 


Can you figure out what these angles would be in radians?
0,1
 2 2


 2 , 2 


 1,0
135°

180°
5
4225°
 2
2


,

 2
2 

 2 2


 2 , 2 


90°

3
4
2
 45°
4
3
2
270°
7
4 315°
0,1
0° 1,0
 2
2


 2 , 2 


Here is the unit circle divided into 12 pieces. Can you
figure out how many degrees are in each division?
 1 3
 , 
 2 2 


 3 1
 , 
 2 2


0,1
120°
90°
1 3
 , 
2 2 


60°
 3 1
 , 
 2 2


150°
30°
 1,0 180°
0° 1,0
210°
 3 1


 2 , 2 


330°
240°
 1
3
  , 
 2 2 


270°
300°
0,1
 3 1
 , 
 2 2


1
3
 , 
2 2 


Can you figure out what the angles would be in radians?
 1 3
 , 
 2 2 


120°
 3 1
 , 
 2 2


 1,0
0,1
1 3
 , 
2 2 


90°
60°
150°

30° 6
180°
30°
 3 1
 , 
 2 2


0° 1,0
210°
 3 1


 2 , 2 


330°
240°
 1
3
  , 
 2 2 


270°
300°
0,1
 3 1
 , 
 2 2


1
3
 , 
2 2 


Assignment
• Take the OPEN NOTE quiz on the weebly
website
– Turn into red basket when completed
• Complete the Unit Circle Quiz worksheet (will
count as a classwork grade not a quiz grade)
– Turn into the red basket
– If not completed in class it is homework!