Parametric Equations and Polar Coordinates

• Parametric Equations[고유주소]

  • Parametric Curve of $C : \begin{cases} x=t^2\\ y=t+1 \end{cases} , \ t\in \mathbb{R}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} x=\cos t \\ y=\sin t \end{cases} , \ 0\le t \le 2\pi$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} x=\sqrt{t} \\ y=t \end{cases} , t\ge 0$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle x=t+ \frac{1}{t} \\ \displaystyle y=t- \frac{1}{t} \end{cases} , t> 0$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle x=2 \sec t \\ \displaystyle y=2 \tan t \end{cases} , \displaystyle -\frac{\pi}{2} < t < \frac{\pi}{2}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle x=t-\sin t \\ \displaystyle y=1-\cos t \end{cases} , t\in \mathbb{R}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} x=t-t^2 \\ y=t-t^3 \end{cases} , \ t\in \mathbb{R}$

    [PDF] [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} x=\cos^3 t \\ y=\sin^3 t \end{cases} , \ 0\le t \le 2\pi$

    [영상(YouTube)] [AlgeoMath]

• Polar Coordinates[고유주소]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{2}{\cos t} \\ \displaystyle \theta= t \end{cases} , \displaystyle - \frac{\pi}{2} < t < \frac{\pi}{2}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{2}{\sqrt{\cos t \sin t}} \\ \displaystyle \theta= t \end{cases} , \ 0 < t < \displaystyle \frac{\pi}{2}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{1}{\sqrt{\cos^2 t -\sin^2 t}} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{4} < t < \frac{\pi}{4}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{1}{1-2\cos t } \\ \displaystyle \theta= t \end{cases} , \ \displaystyle \frac{\pi}{3} < t < \frac{5\pi}{3}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=1-\cos t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=6\sin t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=-\frac{4}{\cos t} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{2} < t < \frac{\pi}{2}$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=4\cos t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$

    [영상(YouTube)] [AlgeoMath]

  • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{4}{2\cos t -\sin t} \\ \displaystyle \theta= t \end{cases} , -\pi+\arctan 2 < t < \arctan 2$

    [영상(YouTube)] [AlgeoMath]

• The Standard Polar Equation [고유주소]

  • 직선에 대한 표준 극좌표 방정식(The Standard Polar Equation for Lines)

    [AlgeoMath]

  • Polar equation for the cricle of radius a centered at $\mathrm{P_0}(r_0,\theta_0)$

    [AlgeoMath]

• 이심률에 의한 원뿔곡선(Conics by eccentricity)

  [영상(YouTube)] [AlgeoMath]

• 이심률에 의한 원뿔곡선(Conics by eccentricity)

  [영상(YouTube)] [AlgeoMath]

• 이심률에 의한 타원(Ellipse by eccentricity)

  [AlgeoMath]

• 이심률에 의한 포물선(Parabola by eccentricity)

  [AlgeoMath]

• 이심률에 의한 쌍곡선(Hyperbola by eccentricity)

  [AlgeoMath]