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Defining curves with parametric equations

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Intros
Lessons
  1. Defining Curves with Parametric Equations Overview:
  2. Sketching Parametric Curves
  3. Eliminating the parameter part 1
  4. Eliminating the parameter part 2
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Examples
Lessons
  1. Sketching Parametric Curves
    Sketch the following parametric curves using table of values and identify the direction of motion:
    1. x=t2−t x=t^2-t
      y=ty=t
    2. x=cos⁡(θ)x= \cos (\theta)
      y=sin⁡(θ)y= \sin (\theta)
    3. x=sin⁡(θ)x= \sin (\theta)
      y=sin⁡(2θ)y= \sin (2\theta) where 0≤θ≤π20 \leq \theta \leq \frac{\pi}{2}
  2. Finding the Cartesian Equation of the Curve
    Eliminate the parameter and find the Cartesian equation of the following curves:
    1. x=t3+1 x=t^3+1
      y=t+3y=t+3
    2. x=ln⁡(2t) x= \ln (2t)
      y=ety=e^t
  3. Find the Cartesian Equation of the Curve with Trigonometric Identities
    Eliminate the parameter θ\theta and find the Cartesian equation of the following curves:
    1. x=sin⁡(2θ)x= \sin (2\theta)
      y=cos⁡(2θ)y= \cos (2\theta)
    2. x=5sin⁡(θ)x= 5\sin (\theta)
      y=3cos⁡(θ)y= 3\cos (\theta)