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Common Core Standard  F.TF.2  High School Geometry
unit circle + -
+  -
For sine count the number of fingers below the folded finger which equals 2.







 45 degrees will be represented by your middle finger.




= 1/2
Square root 1 /2
square root two over two
square root two over two
square root one over two
square root one over two
square root three over two
horizontal line
q1
horizontal line
unit circle - +

Unit Circle Quadrant Two

Unit Circle Quadrant Three

Unit Circle Quadrant Four

arrow down
square root three over two
unit circle quadrant one
o
o
Your hand can be used as a reference to help remember the unit circle

The tips of your fingers remind you that will be taking the square root of the numerator, and your palm reminds you that the denominator will equal two..

See Figure 1. for what each part of hand will represent.

Your pinkie represents 0 degrees,your ring finger equals 30 degrees,the middle finger equals 45, and your pointing finger equals 60 degrees on the Unit Circle.

Cosine is written first, followed by Sine


memorize unit circle hand method
0
2
60
45
30





Square root symbol
hand trick 30 degrees
 quadrant one
hand trick 45 degrees
quadrant 1
hand trick 60 degrees
quadrant 1 unit circle
1
3
2
Folded Finger
1
Folded Finger
Folded Finger
1
1
1
3
2
2
1
2
30 Degrees
60 Degrees
45  Degrees
right arrow
1           0
​Cosine    Sine
​Cosine    Sine
0          1
square root three over two
square root two over two
square root three over two
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
down arrow
arrow
arrow
square root three over two
square root two over two
square root 3 /2
​Cosine    Sine
Cosine    Sine
0          1
1           0
o
o
o
o
o
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one half
1/2

How to remember the Unit Circle

Unit Circle

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Unit Circle Quadrant One

You can remember the trig function values by remembering  

All  Students  Take  Calculus 

A = All positive
S= Sine and it's reciprocal cosecant  are positive
T = Tangent and it's reciprocal cotangent are positive
C = Cosine and it's reciprocal secant are positive
unit circle + +
unit circle - -
+  +
-  +
-  -
​Fold over and remember the correct Trig Values
​Fold down and remember the correct Trig Values
​Fold over and remember the correct Trig Values
C
T
S
A
This is part two of " Easy Way to Remember Unit Circle" The video shows you how to go from Quadrant one to the complete unit Circle
Now let's move from Quadrant one to the rest of the Unit Circle
For sine count the number of fingers below the folded finger which equals 1

For sine count the number of fingers below the folded finger which equals 3.

Use this Math trick as an easy way to remember the unit circle.

Use your hand to help you remember Quadrant 1 of the Unit Circle

Degrees

Radians

Sin

Cosine

Tangent

Cotangent

Secant

Cosecant

0

 

0

0

1

0

undefined

1

undefined

30

π/6

1/2

√3/2

√3/3

√3

2√3/3

2

45

π/4

√2/2

√2/2

1

1

√2

√2

60

π/3

√3/2

1/2

√3

√3/3

2

2√3/3

90

π/2

1

0

Undefined

0

undefined

1

120

2π/3

√3/2

-1/2

-√3

-√3/3

-2

2√3/3

135

3π/4

√2/2

-√2/2

-1

-1

-  √2

√2

150

5π/6

1/2

-√3/2

-√3/3

-√3

-2√3/3

2

180

π

0

-1

0

undefined

-1

undefined

210

7π/6

-1/2

-√3/2

√3/3

√3

-2√3/3

-2

225

5π/4

-√2/2

-√2/2

1

1

-√2

-√2

240

4π/3

-√3/2

-1/2

√3

√3/3

-2

-2√3/3

270

3π/2

-1

0

undefined

0

undefined

-1

300

5π/3

-√3/2

1/2

-√3

-√3/3

2

2√3/3

315

7π/4

-√2/2

√2/2

-1

-1

√2

-√2

330

11π/6

-1/2

√3/2

-√3/3

-√3

2√3/3

-2

360

0

1

0

undefined

1

undefined

 

Trig Functions Chart

trig chart link

Trig Functions Chart

Put it all together and you have the unit circle quadrant one

For Cosine count the number of fingers above the folded finger,which equals 1 finger.
unit circle trig values
unit circle
orange line
orange line/circle
For Cosine count the number of fingers above the folded finger,which is equal to three.
For Cosine count the number of fingers above the folded finger,which equals 2.
Figure 1.
How do you remember the sign values for the four quadrants of the unit circle? 

One easy method is to think of each Quadrant in terms of the x and y axis. 
If you are graphing on a coordinate plane you know all values to the right of the y axis are positive, and values to the left are negative. 
In the same way everything above the x axis has a positive value, and items below the x axis have a negative value. Look at Quadrant 1, all items in this quadrant are right of the y axis, and above the x axis. 
Therefore, the sign values for this Quadrant are (+, +). Remember the x value is always written before the y value. Look at Quadrant 2, all sign values in this Quadrant are left of the y axis, and above the y axis. 
Therefore the values for x are negative, and positive for y values so you write the values (-,+). Quadrant 3 has sign values (-,-) and Quadrant 4 has sign values (+,-).  
​(0,1)
​(0, -1)
value of the unit circle
unit circle and the trig functions
The unit circle has a radius of one. The position (1, 0) is where x has a value of 1, and y has a value of 0. This starting position in the unit circle represents 0 degrees. The position (0,1) represents 90 degrees. The position (-1,0) represents 180 degrees. The position (0, -1) represents 270 degrees. A full circle is 360 degrees and ends at the starting position (0, 1).
 30 degrees will be represented by your ring finger.

60 degrees is represented by your pointing finger.