ap calc

✍️ Free Response Questions (FRQ)

👑 Unit 1: Limits & Continuity

🤓 Unit 2: Differentiation: Definition & Fundamental Properties

🤙🏽 Unit 3: Differentiation: Composite, Implicit & Inverse Functions

👀 Unit 4: Contextual Applications of the Differentiation

✨ Unit 5: Analytical Applications of Differentiation

🔥 Unit 6: Integration and Accumulation of Change

💎 Unit 7: Differential Equations

🐶 Unit 8: Applications of Integration

🦖 Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

♾ Unit 10: Infinite Sequences and Series (BC Only)

🧐 Multiple Choice Questions (MCQ)

#parametricequations

#definition

#derivatives

⏱️ **1 min read**

written by

sumi vora

June 8, 2020

**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:

**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 isn’t actually on the graph; we just use t as our constant so that our points are independent from one another.

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. **

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

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