Paper Plate Intro Unit Circle

Squares with one diagonal create 45–45–90 triangles

Given the length of the legs, find the hypotenuse. Given the hypotenuse find the length of each leg. Make a generalization about relationship between leg and hypotenuse

Equilateral Triangles with an altitude drawn create 30–60–90 triangles

Given length of hypotenuse, find length of short leg and long leg. Make a generalization about relationship between hypotenuse and short leg and long leg.

Hypotenuse 30

Long Horizontal Leg

Short Vertical Leg

1 Short = ( Hypotenuse ) 2 Long = 3 ( Short ) Long Hypotenuse Vertical Leg 60 Short Horizontal Leg

3 = ( Hypotenuse ) 2

45 Hypotenuse

Equal Length Leg

45 Equal Length Leg

Hypotenuse = 2 ( Leg ) Hypotenuse 2 Leg = i 2 2 2 Leg = ( Hypotenuse ) 2

Squares with one diagonal create 45–45–90 triangles

4 2

4

5 2 2

4

3 2 3

5

5 2 2

3

1

1 2 2

1 2 2

Given the length of the legs, find the hypotenuse. Given the hypotenuse find the length of each leg. Make a generalization about relationship between leg and hypotenuse

Equilateral Triangles with an altitude drawn create 30–60–90 triangles

8

4 3 4

1 1 3 2 1 2

3

3 2

3 3 2

1 1 3 2

Given length of hypotenuse, find length of short leg and long leg. Make a generalization about relationship between hypotenuse and short leg and long leg.

1 2

Unit Circle:

Fold your paper within the interior of the circle to find all special angles. Color code the angles with a large dot. Ex. 0-90-180-270 are black, 30s – green, 45s – blue, 60s – red Using a ruler connect origin to each dot using the appropriate color from your coding Label angles in degree measure in the appropriate color. We’ll label radian measures later. Label ( x, y ) coordinates in the appropriate color. Save this unit circle for reference in your Trigonometry class. This will be your most useful paper unit circle ever!!

Unit Circle:

Fold your paper within the interior of the circle to find all special angles.

Degree Radian

ANSWER KEY

( x, y ) = ( cos θ ,sin θ ) ; tan θ

Each special point on the circle has the information

Save this unit circle for reference in your Trigonometry class. This will be your most useful paper unit circle ever!!

120

3π 135 4 ⎛ 2 2⎞ , ⎜⎜ − ⎟⎟ ; − 1 ⎝ 2 2 ⎠

90

2π 3

π

2 ( 0,1) ; und .

⎛ 1 3⎞ 3 ⎜⎜ − , ⎟⎟ ; − 1 ⎝ 2 2 ⎠

π

60

3

⎛1 3⎞ ⎜⎜ , ⎟⎟ ; 2 2 ⎝ ⎠

3 1

5π 6

150

π

45

4 ⎛ 2 2⎞ , ⎜⎜ ⎟⎟ ; 1 2 2 ⎝ ⎠

⎛ 3 1⎞ 1 , ⎟⎟ ; − ⎜⎜ − 3 ⎝ 2 2⎠

0

7π 6 ⎛ 3 1⎞ 1 , − ⎟⎟ ; ⎜⎜ − 2⎠ 3 ⎝ 2 210

5π 4 ⎛ 2 2⎞ ,− ⎜⎜ − ⎟; 1 2 ⎟⎠ ⎝ 2

0

(1, 0 ) ;

0

225

6

⎛ 3 1⎞ 1 , ⎟⎟ ; ⎜⎜ 2 2⎠ 3 ⎝

180 π

( −1, 0 ) ;

π

30

30 ⎛ 3 1⎞ , ⎟⎟ ; ⎜⎜ ⎝ 2 2⎠

4π 3 ⎛ 1 3⎞ ⎜⎜ − , − ⎟⎟ ; 2 2 ⎝ ⎠

300

240

3 1

3π 2 ( 0, −1) ; und . 270

5π 3

⎛1 3⎞ 3 ⎜⎜ , − ⎟⎟ ; − 2 ⎠ 1 ⎝2

0

π 6 1 3

7π 4 ⎛ 2 2⎞ ,− ⎜⎜ ⎟ ; −1 2 ⎟⎠ ⎝ 2 315

Degree Radian

Unit Circle has radius 1 120 3π 135 4 ⎛ 2 2⎞ , ⎜⎜ − ⎟⎟ ; − 1 2 2 ⎝ ⎠

( x, y ) = ( cos θ ,sin θ ) ; tan θ 90

2π 3

π

2 ( 0,1) ; und .

⎛ 1 3⎞ 3 ⎜⎜ − , ⎟⎟ ; − 1 ⎝ 2 2 ⎠

π

60

3

⎛1 3⎞ ⎜⎜ , ⎟⎟ ; ⎝2 2 ⎠

3 1

5π 6

150

π

45

4 ⎛ 2 2⎞ , ⎜⎜ ⎟⎟ ; 1 ⎝ 2 2 ⎠

⎛ 3 1⎞ 1 , ⎟⎟ ; − ⎜⎜ − 3 ⎝ 2 2⎠

0

7π 6 ⎛ 3 1⎞ 1 , − ⎟⎟ ; ⎜⎜ − 2⎠ 3 ⎝ 2 210

5π 4 ⎛ 2 2⎞ ,− ⎜⎜ − ⎟; 1 2 ⎟⎠ ⎝ 2

0

(1, 0 ) ;

0

225

6

⎛ 3 1⎞ 1 , ⎟⎟ ; ⎜⎜ ⎝ 2 2⎠ 3

180 π

( −1, 0 ) ;

π

30

30 ⎛ 3 1⎞ , ⎟⎟ ; ⎜⎜ 2 2⎠ ⎝

4π 3 ⎛ 1 3⎞ ⎜⎜ − , − ⎟; 2 ⎟⎠ ⎝ 2

300

240

3 1

3π 2 ( 0, −1) ; und . 270

5π 3

⎛1 3⎞ 3 ⎜⎜ , − ⎟⎟ ; − 2 ⎠ 1 ⎝2

0

π 6 1 3

7π 4 ⎛ 2 2⎞ ,− ⎜⎜ ⎟⎟ ; − 1 2 2 ⎝ ⎠ 315