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Mathematics Dictionary
Dr. K. G. Shih
Graphics in Analytic Geometry
Questions


  • AN 21 00 | - How to use sketch program ?
  • AN 21 01 | - Reviews
  • AN 21 02 | - Two points and line
  • AN 21 03 | - Graphics of y = sin(n*x)^M
  • AN 21 04 | - Graphs of hyperbolic functions
  • AN 21 05 | - Conics : Circle
  • AN 21 06 | - Conics : parabola
  • AN 21 07 | - Conics : ellipse
  • AN 21 08 | - Conics : hyperbola
  • AN 21 09 | - DeMoivre's theory
  • AN 21 10 | - Graphs of R = a + b*sin(p*A/q)^M
  • AN 21 11 | - Coordinate geometry
  • AN 21 12 | - Transformation
  • AN 21 13 | - Translation
  • AN 21 14 | - Rotation
  • AN 21 15 | - Parametric equations -
    • Answers


    AN 21 01. Review

    Diagram
    • Sketh Programs | Section 1 : Reviews.
    • Contents
      • 1. Number line
      • 2. Abs(x) LT 1 on number line
      • 3. Abs(x) LT 1 on two number lines
      • 4. Compare y = (x^2)/2 with y = -(x^2)/2
      • 5. Compare y = (x^2)/2 with y = -(x^2)/2
      • 6. Compare x^2 - y^2 = -1 and x*y = 1
    Text with examples
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    AN 21 02. Two point and lines

    • Sketh Programs | Section 2 : Two points and lines
    • Functions
      • Enter the program and look the contents
    Text
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    AN 21 03. Graphs of y = sin(n*x)^M
    Program
    • Sketh Programs | Find graphic solutions.
    • Functions
      • 03 01 y = sin(n*x)^M
      • 03 02 y = cos(n*x)^M
    Text
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    AN 21 04. Hyperbolic functions

    Program and contents
    • Sketh Programs | Hyperbolic functions.
    • Functions
      • 04 01 y = sinh(x)
      • 04 02 y = cosh(x)
      • 04 03 y = tanh(x)
      • 04 04 y = csch(x)
      • 04 05 y = sech(x)
      • 04 06 y = coth(x)
    Text
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    AN 21 05. Conics : circle

    Program and contents     Text
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    Q06. Conics : parabola

    Program and contents     Text
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    AN 21 07. Conics : ellipse

    Program and contents     Text
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    AN 21 08. Conics : Hyperbola

    Program and contents
    • Study Program | Conics : Hyperbola
    • Contents
      • Enter the program and look the contents
    Text
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    AN 21 09. DeMoivre's theory

    Program and contents     Text
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    AN 21 10. Graphs of R = a + b*sin(p*A/q)^M

    Program and contents
    • Study Program | Graphs of R = a + b*sin(p*A/q)^M.
    • Contents
      • 10 01 : R = a + b*sin(p*A/q)^M
      • 10 02 : R = a + b*cos(p*A/q)^M
      • 10 03 : R = a + b*tan(p*A/q)^M
      • 10 04 : R = a + b*csc(p*A/q)^M
      • 10 05 : R = a + b*sec(p*A/q)^M
      • 10 06 : R = a + b*cot(p*A/q)^M
    Text
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    AN 21 11. Coordiante geometry

    Program and contents
    • Study Program | Coordiante geometry.
    • Contents
      • Enter the program and see the contents
    Text
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    AN 21 12. Transformation and translation

    Program and contents
    • Study Program | Section 12 : Transformation and translation.
    • Contents
      • 12 01 : It contains 11 demo of transformation matrix
      • 12 02 : It use input to give the matrix
    • Elements of matrix
      • a11 = 1st column and 1st row
      • a21 = 2nd column and 1st row
      • a12 = 1st column and 2nd row
      • a22 = 2nd column and 2nd row
    Text
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    AN 21 13. Translation

    Program and contents
    • Study Program | Translation
    • Functions
      • 13 01 : circle
      • 13 02 : ellipse
      • 13 03 : hyperbola
      • 13 04 : Parabola
    Text
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    AN 21 14. Rotation

    Program and contents
    • Study Program | Rotation
    • Functions
      • 14 01 : Ellipse
      • 14 02 : hyperbola
      • 14 03 : parabola
    Text
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    AN 21 15. Parametric equations

    Program and contents
    • Study Program | Parametric equations
    • Functions
      • x = sin(t) and y = sin(t)
      • x = cos(t) and y = sin(t)
      • x = sec(t) and y = tan(t)
      • x = tan(t) and y = sec(t)
    • Demo : Click re-plot to continue
      • 1. t = 000 to 090 degrees
      • 2. t = 090 to 180 degrees
      • 3. t = 180 to 270 degrees
      • 4. t = 270 to 360 degrees
      • 5. t = 000 to 360 degrees
    Text
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    AN 21 00. How to use sketch program

    • Sketh Programs | Find graphic solutions.
    • 1. Start demo and sketch program
      • Clcik program
      • Select run at current location
      • Select yes to run
    • 2. demo in program 03 02
      • Click Menu command
      • Click section 03 in upper box
      • Click Program 02 in lower box
      • Click re-plot or press Enter to see next demo
    • 3. How change scale and replot ? N/A
      • After we get the graph, we select new xmax and ymax in left box
      • Click replot
    • 4. What is demo command ?
      • Click Menu then click Demo
      • Select a section number
      • Slect a program
      • It will give a plot using default values.
      • For example : What is the function of 01 04 ?
    • 5. What is the meaning of 01 04 ?
      • 1st number is the section number in upper box
      • 2nd number is the function number in lower box

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