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Understanding the Unit Circle with Mrs. Crespo

Explore the unit circle with Mrs. Crespo from Ladywood High School, learn about coordinate points, special triangles, degree and radian measures, and more in this comprehensive guide. Have fun mastering math concepts!

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Understanding the Unit Circle with Mrs. Crespo

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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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