1. Introduction to Parametric Equations and Vectors
Rizzi – Calc BC

2. Parametric Equations
Involve both x and y expressed in terms of a third variable, t
Review: Sketch the following graph.
𝑥= 𝑡 2 −4 and 𝑦= 𝑡 2 , −2≤𝑡≤3

3. What will this graph look like?
𝑥=3 sin 𝑡 and 𝑦=3 cos 𝑡 , 0≤𝑡<2𝜋

4. Let’s Do Some Calculus! Given 𝑥=2 𝑡 and 𝑦=3 𝑡 2 −2𝑡
Find 𝑑𝑦 𝑑𝑥 and 𝑑 2 𝑦 𝑑 𝑥 2 and evaluate at 𝑡=1

5. FYI
Everything you know from chapters 2-5 about derivatives and integrals still applies in these problems
Recall what you know about tangent lines, extrema, and concavity

6. Try This!
Given 𝑥=4 cos 𝑡 and 𝑦=3 sin 𝑡 , write an equation of the tangent line to the curve at point where 𝑡= 3𝜋 4

7. Vectors A vector is a quantity that has both magnitude and direction
Generally written like this: 𝑥 𝑡 , 𝑦 𝑡
Description of x and y both in terms of t

8. Particle Motion
Like above, everything you know about particle motion still applies
The only difference: x and y are defined independently
Particle Motion Free Response Questions framed in terms of
Vectors OR
Parametrics
(But they’re basically the same in how they operate)

9. Position, Speed, Velocity, and Acceleration
A particle moves in the xy-plane so that at any time t, 𝑡≥0, the position of the particle is given by 𝑥 𝑡 = 𝑡 3 +4 𝑡 2 and 𝑦 𝑡 = 𝑡 4 − 𝑡 3
Find the velocity vector at 𝑡=1
Find the speed of the particle at 𝑡=1
Find the acceleration vector at 𝑡=1