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Exercises Trigonometry

Example 9 from Algebra and Trigonometry, 10.6 Parametric Equations

Finding a Set of Parametric Equations for Curves Defined by Rectangular Equations

Find a set of equivalent parametric equations for $y = {(x + 3)}^{2} + 1.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
An obvious choice would be to let $x (t) = t .$ Then $y (t) = {(t + 3)}^{2} + 1.$ But let’s try something more interesting. What if we let $x = t + 3 ?$ Then we have
$\begin{array}{l} y = {(x + 3)}^{2} + 1 \\ y = {((t + 3) + 3)}^{2} + 1 \\ y = {(t + 6)}^{2} + 1 \end{array}$
The set of parametric equations is

$\begin{array}{l} x (t) = t + 3 \\ y (t) = {(t + 6)}^{2} + 1 \end{array}$
See Figure 9.

Figure 9

How did it go?

PreviousFinding a Cartesian Equation Using Alternate Methods Next Sketching the Graph of a Pair of Parametric Equations by Plotting Points

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.6, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.