11.1.1 Parametric Equations (unfinished: 1 card left)

Parametric Equations

a pair of equations in the same variable

• ex. pair of equations: [x = f(t), y = g(t)]

Parameter

the variable shared between two separate functions

• ex. if the pair of equations are x = f(t) and y = g(t), t is the parameter

Parametric Curve

The graph that is represented by the set of points (x, y) = (f (t), g(t))

Parametrization

the parametric equations that belong to the curve

It’s more about the steps than the correct answer. What are the steps to solve a question like this?

1. To verify, substitute each variable w/ its corresponding parametric equation

2. ∵ they are equal to the original function, it is a parametrization

3. plot + graph

It’s more about the steps than the correct answer. What are the steps to solve a question like this?

1. To verify, substitute each variable w/ its corresponding parametric equation

2. ∵ they are equal to the original function, it is a parametrization

3. plot + graph

Orientation. How is it indicated?

1. the direction in which the points on a parametric curve are plotted as the parameter increases

2. indicated by arrows on the curve pointing in the direction of the orientation

What can be noticed when compared to Example 1 which had the same graphical response?

1. make table then plot points

by adding, more values it slows down how fast the points move around the curve

Using this picture as a guide, in these flashcards, what is an assumption that we have been making? In other words, what could be a problem with this function?