8. Parametric Equations

Question 1

Parametric to Cartesian

Answer 1

Find t in terms of x
Substitute into the y equation

You can do it the other way around if easier/specified

Question 2

Domain of a parametric

Answer 2

The range of the function for x

Question 3

Range of a parametric

Answer 3

The range of the function for y

Question 4

Trig identities for cos and sin

Answer 4

Can write cos t, sin t in terms of x and y and use cos^2 + sin^2 = 1

Or similar with reciprocal identities

Question 5

Sketching parametrics

Answer 5

Make a table of x and y for values of t in the domain and sketch

Question 6

Finding points of intersection with a Cartesian

Answer 6

Substitute x and y from the parametric into the Cartesian and solve or show it can’t be