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Published byLeona Scott Modified over 9 years ago
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x y 0 radians 2 radians radians radians radius = 1 unit(1,0) (0,1) (-1,0) (0,-1) (1,0)
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0 22 x y radians 45 x 1 y x 2 + y 2 = 1 2 In a 90-45-45 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.
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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 =
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60 0 y The 3 red lines divide the circle (2 ) into 6 equal parts. 2 6 = 60 1 In a 90-60-30 right triangle the side opposite the 30 angle is one-half the hypotenuse. 1 y ( ) 2 + y 2 = 1 2 + y 2 = 1 y 2 = 1 - y 2 = y = =
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x y 0 (+,+)(-,+) (-,-)(+,-) This family of points have identical order pairs except that the signs change according to the Quadrant occupied by the point.
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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.
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30° 1 In a 90-60-30 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
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0 22 (1,0) (0,1) (-1,0) (0,-1) (1,0)
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