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Mathematics Dictionary
Dr. K. G. Shih
Trigonometry Diagrams
Questions


  • TR 21 00 | - How to use sketch program ?
  • TR 21 01 | - Figures in trigonometry
  • TR 21 02 | - Graphs of trigonometrical functions
  • TR 21 03 | - Trigonometric functions in form of y = F(n*x)^M
  • TR 21 04 | - Inverse trigonometric functions
  • TR 21 05 | - Star Functions
  • TR 21 06 | - Special Functions
  • TR 21 07 | - Trigonometric equations
  • TR 21 08 | - Transformations of y = sin(x) and y = cos(x)
  • TR 21 09 | - Parametric equations
  • TR 21 10 | - Flower functions
  • TR 21 11 | -
  • TR 21 12 | -
    • Answers


    TR 21 01. Polynomial Functions and equations
    • Sketh Programs | Find graphic solutions.
    • Figures
      • 01 01 Sector and angle measurment
      • 01 02 Triangle for trig ratios
      • 01 03 Right triangle with 30 degrees angle
      • 01 04 Angles in 4 quadrant
      • 01 05 Functions relations
      • 01 06 Prove addition formula by cosine law
      • 01 07 Angles A+B and A-B
      • 01 08 Chord function
      • 01 09 Solve x^n - 1 = 0
      • 01 10 Angles and sides of triangle
      • 01 11 Es-circle
      • 01 19 Pedal triangle

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    TR 21 02. Trig Functions

    • Sketh Programs | Find graphic solutions.
    • Functions
      • 02 01 y = sin(x)
      • 02 02 y = cos(x)
      • 02 03 y = tan(x)
      • 02 04 y = csc(x)
      • 02 05 y = sec(x)
      • 02 06 y = cot(x)
      • 02 07 y = sin(x) and y = csc(x)
      • 02 08 y = cos(x) and y = sec(x)
    • Example : Find the range of y = sin(x) for x between -360 and 360
      • Start sketch programs
      • Click Menu command
      • Click Section 02 of trig functions in upper box
      • Click program 01 y = sin(x) in lower box
      • No data is required
    • Exercises
      • Find asymptotes of y = tan(x) for x between -360 anf 360

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    tr 21 03. Functions y = F(n*x)^M
    • Sketh Programs | Find graphic solutions.
    • Functions
      • 03 01 y = sin(n*x)^M
      • 03 02 y = cos(n*x)^M
      • 03 03 y = tan(n*x)^M
      • 03 04 y = csc(n*x)^M
      • 03 05 y = sec(n*x)^M
      • 03 06 y = cot(n*x)^M
    • Example : Find the graph of y = sin(1*x)^3 for x between -360 and 360
      • Start sketch programs
      • Click Menu command
      • Click Section 03 of trig functions in upper box
      • Click program 01 y = sin(1*x)^3 in lower box
      • Give coeff n and power M : 1, 3
    • Exercises
      • Graph of y = cos(2*x)^3 for x between -360 anf 360

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    TR 21 04. Inverse trig functions

    • Sketh Programs | Find graphic solutions.
    • Functions
      • 04 01 y = arcsin(x)
      • 04 02 y = arccos(x)
      • 04 03 y = arctan(x)
      • 04 04 y = arccsc(x)
      • 04 05 y = arcsec(x)
      • 04 06 y = arccot(x)
    • Example : Study y = arcsin(x)
      • Start sketch programs
      • Click Menu command
      • Click Section 04 of inverse trigonometric functions in upper box
      • Click program 01 y = arcsin(x) in lower box
      • No data is required
    • Exercises
      • Prove that sin(arcsin(x) = x
      • Prove arcsin(x) = arctan(x/Sqr(1-x^2)

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    TR 21 05. Star functions

    • Sketh Programs | Find graphic solutions.
    • Functions
      • 05 01 R = 1 + sec(p*A/4)^1
      • 05 02 R = 1 + sec(p*A/4)^2
      • 05 03 R = 1 + sec(p*A/4)^3
      • 05 04 R = 1 + sec(p*A/4)^4
    • Example : Study graph of R = 1 + 1*sec(9*A/4)^3
      • Start sketch programs
      • Click Menu command
      • Click Section 05 of star functions in upper box
      • Click program 03 R = 1 + sec(p*A/4)^3 in lower box
      • No data is required
    • Exercises
      • Find the cycle domain of R = 1 + sec(p*A/4)^1

    Go to Begin

    TR 21 06. Special functions

    • Sketh Programs | Find graphic solutions.
    • Functions
      • 06 01 y = sin(a*x) + cos(b*x)
      • 06 02 y = sin(x)/x
      • 06 03 y = cos(x)/x
      • 06 04 y = tan(x)/x
      • 06 05 y = sin(x) + sin(2*x) + sin(3*x)
      • 06 06 y = x*sin(x)
      • 06 07 y = x*cos(x)
    • Example : Study graph of y = sin(x) + cos(2*x)
      • Start sketch programs
      • Click Menu command
      • Click Section 06 of functions in upper box
      • Click program 01 y = sin(x) + cos(2*x) in lower box
      • Data : 1, 2
    • Exercises
      • Solve sin(x) + cos(x) = 1 graphically

    Go to Begin

    TR 21 07. Trigonometric equations

    • Sketh Programs | Find graphic solutions.
    • Equations
      • 07 01 sin(x) = a
      • 07 02 cos(x) = a
      • 07 03 tan(x) = a
      • 07 04 csc(x) = a
      • 07 05 sec(x) = a
      • 07 06 cot(x) = a
    • Example : Solve sin(x) = 0.5 for x between -360 and 360
      • Start sketch programs
      • Click Menu command
      • Click Section 07 of functions in upper box
      • Click program 01 sin(x) = a in lower box
      • Data : 0.5
    • Exercises
      • Solve sin(x) = -0.5 graphically

    Go to Begin

    TR 21 08. Transformation of y = sin(x) to y - d = a*sin(b*x +c*pi)

    • Sketh Programs | Find graphic solutions.
    • Equations
      • 08 01 y - d = a*sin(b*x + c*pi)
      • 08 02 y - d = a*cos(b*x + c*pi)
    • Example : Sketch y - 3 = 2*sin(2*x + 0.25*pi)
      • Start sketch programs
      • Click Menu command
      • Click Section 10 in upper box
      • Click program 01 in lower box
      • Data a, b, c, d : 2, 2, 0.25, 3
    • Exercises : In example
      • 1. what is the amplitude ?
      • 2. What is the period ?
      • 3. What is the equation of sinuoide ?

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    TR 21 09. Parametric equations

    • Sketh Programs | Find graphic solutions.
    • Functions
      • 09 01 x = sin(t) and y = F(t)
      • 09 02 x = cos(t) and y = F(t)
      • 09 03 x = tan(t) and y = F(t)
      • 09 04 x = csc(t) and y = F(t)
      • 09 05 x = sec(t) and y = F(t)
      • 09 06 x = cot(t) and y = F(t)
    • Example : Study graph of x = tan(t) and y = sec(t)
      • Start sketch programs
      • Click Menu command
      • Click Section 09 of parametic functions in upper box
      • Click program 03 in lower box
      • Data for y = F(t) = sec(t) : 5
    • Exercises : Find the similarity and difference of following graphs
      • 1. Graph of x = tan(t) and y = sec(t)
      • 2. Graph of x = sec(t) and y = tan(t)

    Go to Begin

    TR 21 10. Flower function

    • Sketh Programs | Find graphic solutions.
    • Functions
      • 10 01 R = sin(p*A/4)^1
      • 10 02 R = sin(p*A/4)^2
      • 10 03 R = sin(p*A/4)^3
      • 10 04 R = sin(p*A/4)^4
      • 10 05 R = 1 + sin(p*A/4)^1
      • 10 06 R = 1 + sin(p*A/4)^2
      • 10 07 R = 1 + sin(p*A/4)^3
      • 10 08 R = 1 + sin(p*A/4)^4
    • Example : Study graph of R = 1 + 1*sin(9*A/4)^3
      • Start sketch programs
      • Click Menu command
      • Click Section 10 of star functions in upper box
      • Click program 07 R = 1 + sin(p*A/4)^3 in lower box
      • No data is required
    • Exercises
      • Find the cycle domain of R = 1 + sin(p*A/4)^1

    Go to Begin

    Q00. How to use sketch program

    • Sketh Programs | Find graphic solutions.
    • 1. Start sketch program
      • Clcik sketch program
      • Select run at current location
      • Select yes to run
    • 2. Sketch y = sin(x) in 02 01
      • Click Menu command
      • Click polynomial function in section 2 in upper box
      • Click Program 01 in lower box
    • 3. How to change scale and replot ?
      • 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

    Go to Begin
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    Copyright © Dr. K. G. Shih, Nova Scotia, Canada.
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