Example 4 from Algebra and Trigonometry, 10.7 Parametric Equations: Graphs

Graphing Parametric Equations and Rectangular Equations on the Coordinate System

Graph the parametric equations $x = t + 1$ and $y = \sqrt{t},$ $t \geq 0,$ and the rectangular equivalent $y = \sqrt{x - 1}$ on the same coordinate system.

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
Construct a table of values for the parametric equations, as we did in the previous example, and graph $y = \sqrt{t},$ $t \geq 0$ on the same grid, as in Figure 6.

Figure 6

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Sketch the graph of the parametric equations $x = 2 \cos θ and y = 4 \sin θ,$ along with the rectangular equation on the same grid.

How did it go?

Solution

Your turn

Solution

Your turn