How to sketch parametric curves and their orientation

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In this video we talk about how to sketch a parametric curve by plotting points along the curve as the parameter value changes.

Keep in mind that parametric curves are different than cartesian curves. Cartesian curves are defined in terms of x and y and can therefore be sketched in rectangular coordinate space.

On the other hand, parametric curves are defined by two equations; one for x in terms of t and the other for y in terms of t, assuming t is the parameter value. Therefore, when we want to sketch a parametric curve, we have to sketch it at all times in relation to the parameter value t.

The orientation of the parametric curve will be based on the direction of increasing t. So whenever we sketch a parametric curve, we have to indicate the direction of increasing t by drawing small direction arrows along the graph.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”