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The unit circle in a jiff

The unit circle in a jiff. By Mrs. Crespo Mathematics Department Ladywood High School. The coordinate points. The Special Triangles (Not Drawn to Scale). The Unit Circle P( x,y )=P( cos θ , sin θ ). (0,1). (- ½ , √3 / 2 ). ( ½ , √3 / 2 ). 60 ˚. 2S. (1 / √2 , 1 / √2 ).

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The unit circle in a jiff

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  1. The unit circle in a jiff By Mrs. Crespo Mathematics Department Ladywood High School

  2. Thecoordinatepoints The Special Triangles (Not Drawn to Scale) The Unit Circle P(x,y)=P(cosθ, sin θ) (0,1) (-½ ,√3/2) (½ ,√3/2) 60˚ 2S (1/√2 , 1/√2 ) ( -1/√2 , 1/√2 ) S S√2 S (√3/2 , ½ ) (-√3/2 , ½ ) 30˚ 45˚ S√3 S (-1,0) (1,0) (-√3/2 , -½ ) (√3/2 , -½ ) (-1/√2 , -1/√2 ) (1/√2 , -1/√2 ) (-½ ,-√3/2) (½ ,-√3/2) (0,-1) (denominators not rationalized) QI (+,+) QII (-,+) QIII (-,-) QIV (+,-) I. Crespo

  3. The degree measures From 0˚ add 90˚ each time until 360˚. From 0˚ add 45˚ each time until 315˚. From 0˚ add 30˚ each time until 330˚. 90˚ 120˚ 60˚ 135˚ 45˚ 150˚ 30˚ 180˚ 0˚ 360˚ 210˚ 330˚ 225˚ 315˚ 240˚ 300˚ 270˚ The Unit Circle I. Crespo

  4. The radian measures We know π = 180˚ Famous stops: 0, π/2, π, 3π/2, 2π π/2 2π/3 π/3 3π/4 π/4 1 1+6 1 1+4 5π/6 π/6 1 1+3 π 0 1 6-1 2π 1 4-1 11π/6 7π/6 1 3-1 5π/4 7π/4 5+6 4π/3 5π/3 3+4 3π/2 2+3 The Unit Circle I. Crespo

  5. The Unit Circle (0,1) (-½ ,√3/2) (½ ,√3/2) (1/√2 , 1/√2 ) ( -1/√2 , 1/√2 ) π/2 2π/3 π/3 90˚ 120˚ 60˚ 3π/4 π/4 135˚ 45˚ (√3/2 , ½ ) (-√3/2 , ½ ) 5π/6 150˚ π/6 30˚ 180˚ 0˚ (-1,0) (1,0) π 0 360˚ 2π 210˚ 330˚ 11π/6 7π/6 (-√3/2 , -½ ) 225˚ 315˚ (√3/2 , -½ ) 240˚ 300˚ 5π/4 270˚ (-1/√2 , -1/√2 ) (1/√2 , -1/√2 ) 4π/3 5π/3 (-½ ,-√3/2) 3π/2 (½ ,-√3/2) (0,-1) I. Crespo

  6. Have fun! I. Crespo

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