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  # 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.
  Short
  Hypotenuse
  Vertical
  30 Long Leg
  Horizontal
  Leg
  
  1
  Short = ( Hypotenuse )
  2
  Long = 3 ( Short )
  3
  Long
  = ( Hypotenuse )
  2
  Hypotenuse Vertical
  Leg
  60
  Short
  Horizontal
  Leg
  45
  Equal
  Hypotenuse
  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 5 2
  4 5
  2
  4 5 2
  2
  
  1 2
  3 2 1
  3 2
  3 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 3 3 3
  4 3
  2
  3
  4
  2
  1 1
  1 1 3 1 3 2
  2 2
  1
  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.
  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.
  
  ## Each special point on the circle has the information
  
  ( x, y ) = ( cos θ ,sin θ ) ; tan θ
  
  Save this unit circle for reference in your Trigonometry class. This will be your most useful paper unit circle ever!!
  
  π
  90
  2π 2 π
  120 60
  3 ( 0,1) ; und . 3
  3π ⎛ 1 3⎞ π
  135 3 ⎛1 3⎞ 3 45
  4 ⎜⎜ − , ⎟⎟ ; − ⎜⎜ , ⎟⎟ ; 4
  ⎝ 2 2 ⎠ 1
  ⎝ 2 2 ⎠ 1
  ⎛ 2 2⎞ ⎛ 2 2⎞
  ⎜⎜ − , ⎟⎟ ; − 1 ⎜⎜ , ⎟⎟ ; 1
  ⎝ 2 2 ⎠ ⎝ 2 2 ⎠
  
  5π π
  150 30
  6 6
  ⎛ 3 1⎞ 1 ⎛ 3 1⎞ 1
  ⎜⎜ − , ⎟⎟ ; − ⎜⎜ , ⎟⎟ ;
  ⎝ 2 2⎠ 3 ⎝ 2 2⎠ 3
  
  180 π 0 0
  ( −1, 0 ) ; 0 (1, 0 ) ; 0
  
  7π π
  210 30
  6 6
  ⎛ 3 1⎞ 1 ⎛ 3 1⎞ 1
  ⎜⎜ − , − ⎟⎟ ; ⎜⎜ , ⎟⎟ ;
  ⎝ 2 2⎠ 3 ⎝ 2 2⎠ 3
  
  5π 7π
  225 315
  4 4π 5π 4
  240 300
  ⎛ 2 2⎞ 3 3 ⎛ 2 2⎞
  ⎜⎜ − ,− ⎟; 1 ⎛ 1 3⎞ ⎛1 3⎞ ⎜⎜ ,− ⎟ ; −1
  ⎝ 2 2 ⎟⎠ 3 3π 3
  ⎝ 2 2 ⎟⎠
  ⎜⎜ − , − ⎟⎟ ; 270 ⎜⎜ , − ⎟⎟ ; −
  ⎝ 2 2 ⎠ 1 2 ⎝2 2 ⎠ 1
  ( 0, −1) ; und .
  ( x, y ) = ( cos θ ,sin θ ) ; tan θ
  π
  90
  2π 2 π
  120 60
  3 ( 0,1) ; und . 3
  3π ⎛ 1 3⎞ π
  135 3 ⎛1 3⎞ 3 45
  4 ⎜⎜ − , ⎟⎟ ; − ⎜⎜ , ⎟⎟ ; 4
  ⎝ 2 2 ⎠ 1
  ⎝2 2 ⎠ 1
  ⎛ 2 2⎞ ⎛ 2 2⎞
  ⎜⎜ − , ⎟⎟ ; − 1 ⎜⎜ , ⎟⎟ ; 1
  ⎝ 2 2 ⎠ ⎝ 2 2 ⎠
  
  5π π
  150 30
  6 6
  ⎛ 3 1⎞ 1 ⎛ 3 1⎞ 1
  ⎜⎜ − , ⎟⎟ ; − ⎜⎜ , ⎟⎟ ;
  ⎝ 2 2⎠ 3 ⎝ 2 2⎠ 3
  
  180 π 0 0
  ( −1, 0 ) ; 0 (1, 0 ) ; 0
  
  7π π
  210 30
  6 6
  ⎛ 3 1⎞ 1 ⎛ 3 1⎞ 1
  ⎜⎜ − , − ⎟⎟ ; ⎜⎜ , ⎟⎟ ;
  ⎝ 2 2⎠ 3 ⎝ 2 2⎠ 3
  
  5π 7π
  225 315
  4 4π 5π 4
  240 300
  ⎛ 2 2⎞ 3 3 ⎛ 2 2⎞
  ⎜⎜ − ,− ⎟; 1 ⎛ 1 3⎞ ⎛1 3⎞ ⎜⎜ ,− ⎟⎟ ; − 1
  ⎝ 2 2 ⎟⎠ 3 3π 3 2 2
  ⎜⎜ − , − ⎟; ⎜⎜ , − ⎟⎟ ; − ⎝ ⎠
  2 ⎟⎠
  270
  ⎝ 2 1 2 ⎝2 2 ⎠ 1
  ( 0, −1) ; und .