Defining curves with parametric equations

Lessons

• Introduction
  Defining Curves with Parametric Equations Overview:
  a)

  Sketching Parametric Curves
  
  
  b)

  Eliminating the parameter part 1
  
  
  c)

  Eliminating the parameter part 2
  
  

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• 1.
  Sketching Parametric Curves
  Sketch the following parametric curves using table of values and identify the direction of motion:
  a)

  $x=t^2-t$

  $y=t$
  
  
  b)

  $x= \cos (\theta)$

  $y= \sin (\theta)$
  
  
  c)

  $x= \sin (\theta)$

  $y= \sin (2\theta)$ where $0 \leq \theta \leq \frac{\pi}{2}$
  
  

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• 2.
  Finding the Cartesian Equation of the Curve
  Eliminate the parameter and find the Cartesian equation of the following curves:
  a)

  $x=t^3+1$

  $y=t+3$
  
  
  b)

  $x= \ln (2t)$

  $y=e^t$
  
  

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• 3.
  Find the Cartesian Equation of the Curve with Trigonometric Identities
  Eliminate the parameter $\theta$ and find the Cartesian equation of the following curves:
  a)

  $x= \sin (2\theta)$

  $y= \cos (2\theta)$
  
  
  b)

  $x= 5\sin (\theta)$

  $y= 3\cos (\theta)$
  
  

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