Counter
Mathematics Dictionary
Dr. K. G. Shih
Parametric equations
Subjects


  • Q01 | - Parametric equations
  • Q02 | - Unit circle : x^2 + y^2 = 1
  • Q03 | - Unit hyperbola : x^2 - y^2 = 1
  • Q04 | - Compare x^2 - y^2 = 1 and x^2 - y^2 = -1
  • Q05 | - E
  • Q06 | - F
  • Q07 | - G
  • Q08 | - H
  • Q09 | - I
  • Q10 | - J
  • Q11 | - K
  • Q12 | - L
  • Q13 | - M
  • Q14 | - N
  • Q15 | - O
  • Q16 | - P
  • Q17 | - Q
  • Q18 | - R
  • Q19 | - S
  • Q20 | - T
  • Q21 | - U
  • Q22 | - V
  • Q23 | - W
  • Q24 | - X
  • Q25 | - Y
  • Q26 | - Z
    • Answers


    Q01. Parametric equations
    Equations
    • 1. x = sin(t) and y = cos(t).
    • 2. x = cos(t) and y = sin(t).
    • 3. x = tan(t) and y = sec(t).
    • 4. x = sec(t) and y = tan(t).
    Diagrams
    • Subject | Diagrams of parametric equations
    • Study topic
      • Find the curve of x = tan(t) and y = sec(t).
      • Find the curve of x = sec(t) and y = tan(t).
      • Describe the difference.

    Go to Begin

    Q02. Unit circle

    Equation of circle
    • (x - h)^2 + (y - k)^2 = r^2.
    • Where (h, k) is the center and r is the radius.
    Unit circle
    • Center at (0,0) and radius = 1.
    • Equation : x^2 + y^2 = 1.
    Prove that x = cos(t) and y = sin(t) is unit circle when t goes from 0 to 2*pi.
    • x^2 + y^2 = cos(t)^2 + sin(t)^2.
    • Since cos(t)^2 + sin(t)^2 = 1.
    • Hence x^2 + y^2 = 1 is unit circle.
    Waht is the graph of x = sin(t) and y = cos(t) ?
    • It is unit circle.

    Go to Begin

    Q03. Unit hyperbola

    Equation of hyperbola
    • ((x - h)/a)^2 + ((y - k)/b)^2 = 1.
    • Where (h, k) is the center.
    • a and b are the semi-axese.
    Unit hyperbola
    • Center at (0,0), a = 1, and b = 1.
    • Equation : x^2 - y^2 = 1.
    Prove that x = sec(t) and y = tan(t) is unit hyperbola when t goes from 0 to 2*pi.
    • x^2 - y^2 = sec(t)^2 - tan(t)^2.
    • Since 1 + tan(t)^2 = sec(t)^2.
    • Hence x^2 - y^2 = 1 is unit hyperbola.
    Waht is the graph of x = tan(t) and y = sec(t) ?
    • x^2 - y^2 = tan(t)^2 - sec(t)^2.
    • Since 1 + tan(t)^2 = sec(t)^2. Hence tan(t)^2 - sec(t)^2 = -1.
    • Hence x^2 - y^2 = -1 is also unit hyperbola.

    Go to Begin

    Q04. Compare x^2 - y^2 = 1 and x^2 - y^2 = -1
    Equations x^2 - y^2 = 1
    • Vertex of heyperbola are at x = -1 and x = +1.
    • Principal axis is y = 0.
    • Foci = Sqr(a^2 + b^2) = Sqr(2).
    • Asymptotes : y = x and y = -x.
    Equations x^2 - y^2 = -1
    • Vertex of heyperbola are at y = -1 and y = +1.
    • Principal axis is x = 0.
    • Foci = Sqr(a^2 + b^2) = Sqr(2).
    • Asymptotes : y = x and y = -x.

    Go to Begin

    Q05. E

    Go to Begin

    Q06. F


    Go to Begin

    Q07. G


    Go to Begin

    Q08. H

    Go to Begin

    Q09. I

    Show Room of MD2002 Contact Dr. Shih Math Examples Room
    Copyright © Dr. K. G. Shih, Nova Scotia, Canada.
    1