x y 0 radians 2  radians  radians radians radius = 1 unit(1,0) (0,1) (-1,0) (0,-1) (1,0)

0 22 x y  radians 45  x 1 y x 2 + y 2 = 1 2 In a triangle x = y therefore: x 2 + x 2 = 1 2 2x 2 = 1 x 2 = x = x = y = In Quadrant I both x and y are positive.

radians 0 In Quadrant II x is negative and y is positive. In Quadrant III x is negative and y is negative. In Quadrant IV x is positive and y is negative. (+,+)(-,+) (-,-)(+,-) By dividing each quadrant in half, four more points around the 2  radians making one circle are identified. The 2  has been divided into eight equal parts. 2   8 =

60  0 y The 3 red lines divide the circle (2  ) into 6 equal parts. 2   6 = 60  1 In a right triangle the side opposite the 30  angle is one-half the hypotenuse. 1 y ( ) 2 + y 2 = y 2 = 1 y 2 = 1 - y 2 = y = =

x y 0 (+,+)(-,+) (-,-)(+,-) This family of points have identical order pairs except that the signs change according to the Quadrant occupied by the point.

2   12 = Of all of the angles discussed thus far only 4 of them are not in the diagram shown above. By using the lines from the last family and new blue intersecting lines, the circle is divided into 12 congruent angles.

30° 1 In a right triangle the side opposite the 30  angle is one-half the hypotenuse. x 2 + ( ) 2 = 1 2 x 2 + = 1 x 2 = 1 - x 2 = x = = x (+,+)(-,+) (-,-)(+,-) 30° 1

0 22  (1,0) (0,1) (-1,0) (0,-1) (1,0)