Mathematics Dictionary
Dr. K. G. Shih

    Figure 325 : R = sin(2*A) and R = cos(2*A)


  • Q01 | - Diagram : R = sin(2*A) and R = cos(2*A)
  • Q02 | - Compare : R = sin(2*A) and R = cos(2*A) between A = 90 and 180
  • Q03 | - Reference

    Q01. Diagram : R = sin(2*A) and R = cos(2*A)


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    Q02. Compare R = sin(2*A) and R = cos(2*A) between 90 and 180

    R = sin(A) and = 90 to 180 degrees
    • The angle A is in 2nd quadrant
    • The angle 2*A is between 180 and 360
    • Hence R = sin(2*A) are negative values
    • The plot angles
      • A = 090 and R = -0, plot angle = 090 + 180 = 270
      • A = 135 and R = -1, plot angle = 135 + 180 = 315
      • A = 180 and R = -0, plot angle = 180 + 180 = 360
      • Hence curve is in 4th quadrant
    • Hence plot angles are between 270 and 360
    • Hence the sketch is in 4th quadrant

      • Angle A ......... 90 ..... 120 .... 135 ...... 150 .... 180
      • Angle 2*A ...... 180 ..... 240 .... 270 ...... 300 .... 360
      • R=sin(2*A) ...... -0 ... -0.86 ..... -1 .... -0.86 ..... -0
      • Sketch angle ... 270 ..... 300 .... 315 ...... 330 .... 360
      • The curve is from 270 to 360 in 4th quadrant

    R = cos(A) and = 90 to 180 degrees
    • The angle A is in 2nd qudrant
    • The angle 2*A is between 180 and 360
    • The R = cos(2*A) are negative when 2*A between 180 and 270
    • Hence plot angle for A between 90 and 135
      • A = 090 and R = -1, plot angle = 090 + 180 = 270
      • A = 135 and R = -0, plot angle = 135 + 180 = 315
      • Hence curve is in 4th quadrant
    • Hence plot angle for A between 135 and 180
      • A = 135 and R = +0, plot angle = 135
      • A = 180 and R = +1, plot angle = 180
      • Hence curve is in 2nd quadrant
    • The R values are positve when 2*A between 270 and 360
    • Hence plot angle is between 90 and 180 (2nd quadrant)
    • Hence the sketch is in 2nd and 4th quadrants

      • Angle A .......... 90 .... 120 .... 135 ...... 150 .... 180
      • Angle 2*A ....... 180 .... 240 .... 270 ...... 300 .... 360
      • R=cos(2*A) ...... -1 ....-0.5 ..... +0 ..... +0.5 ..... +1
      • Sketch angle .... 270 .... 300 .... 135 ...... 150 .... 180
      • Sketch angle .... 270 .... 300 .... 315
      • The plot in 4th quadrant 270 to 315 then from 135 to 180 in 2nd quadrant

    Note
    • 1. The cyclic domain : A = 0 to 360 degrees
    • 2. Plot angle is A + 180 if R is negative

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    Q03. Reference

    Book
    • Pattern mathematics by Dr. Shih
    Computer program
    Go to Begin
    • Show Room of MD2002 Contact Dr. Shih Math Examples Room
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