ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

9.1 Defining and Differentiating Parametric Equations

#parametricequations

#definition

#derivatives

โฑ๏ธย ย 1 min read

written by

Sumi Vora

sumi vora


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What is a Parametric Function?ย 

Parametric functions are a set of related functions where x and y are independent from each other, but they are connected using the dummy variable t, which represents time. When we use the cartesian graph, we assume that we are moving along the x-axis in only one direction at a constant rate. However, parametric equations give us more freedom to manipulate horizontal motion.

A parametric equation would look something like this:ย 

x(t) = t^2 - 1, y(t) = 3t

In this equation, your x-coordinate would be determined by t^2-1 and your y-coordinate would be determined by 3t. So, when t = 1, you would plot the point (0, 3). In a parametric function, t isnโ€™t actually on the graph; we just use t as our constant so that our points are independent from one another.ย 

Derivatives of Parametric Functions

Like we discussed earlier, a parametric function is still graphed in 2D on an xy-plane, so if we wanted to find the slope of the tangent line, we would still need to find dy/dx

If we divide dx/dt and dy/dt, then dt will cancel out.ย 

(dy/dt)/(dx/dt) = dy/dx

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