NSW Y11 Maths - Extension 1 Functions Parametric Form

Resources for Parametric Form

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Parametric Form Theory

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  • Parametric Form - Video - Parametric Equations in 7 minutes

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Theory

\(x = f(t),\,y = g(t)\,\,{\rm{or }}x = f(\theta ),\,y = g(\theta )\) are parametric forms and are another technique in representing a function.

For example, the parabola \(y = \dfrac{1}{4}{x^2}\) in the cartesian form can be represented in the parametric form as \(x = 2t,\,y = {t^2}\) and by substituting values for \(t\) the parabola can be graphed.

Another example is the circle \({x^2} + {y^2} = 1\) in the cartesian form can be represented in the parametric form by \(x = \cos \theta ,\,\,y = \sin \theta \).

Syllabus Reference

NSW Syllabus Reference: ME-F1.4 Parametric form of a function or relation. This will require student to 

  • understand the concept of parametric representation and examine lines, parabolas and circles expressed in parametric form
    • understand that linear and quadratic functions, and circles can be expressed in either parametric form or Cartesian form
    • convert linear and quadratic functions, and circles from parametric form to Cartesian form and vice versa
    • sketch linear and quadratic functions, and circles expressed in parametric form

Ref: https://educationstandards.nsw.edu.au/