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# Unit: Parametric equations, polar coordinates, and vector-valued functions

#### 0

Possible mastery points

## Parametric equations intro

Practice
Parametric equations differentiationGet 3 of 4 questions to level up!

## Second derivatives of parametric equations

Practice
Second derivatives (parametric functions)Get 3 of 4 questions to level up!

## Arc length: parametric curves

Practice
Parametric curve arc lengthGet 3 of 4 questions to level up!

#### Quiz 1

Level up on the above skills and collect up to 300 Mastery points

## Vector-valued functions

Practice
Vector-valued functions differentiationGet 3 of 4 questions to level up!
Second derivatives (vector-valued functions)Get 3 of 4 questions to level up!

#### Quiz 2

Level up on the above skills and collect up to 200 Mastery points

## Planar motion

Practice
Planar motion (differential calc)Get 3 of 4 questions to level up!
Motion along a curve (differential calc)Get 3 of 4 questions to level up!
Planar motion (with integrals)Get 3 of 4 questions to level up!

#### Quiz 3

Level up on the above skills and collect up to 300 Mastery points

## Polar functions

Practice
Differentiate polar functionsGet 3 of 4 questions to level up!
Tangents to polar curvesGet 3 of 4 questions to level up!

## Area: polar regions (single curve)

Practice
Area bounded by polar curves introGet 3 of 4 questions to level up!
Area bounded by polar curvesGet 3 of 4 questions to level up!

## Area: polar regions (two curves)

Practice
Area between two polar curvesGet 3 of 4 questions to level up!

## Arc length: polar curves

Practice
Arc length of polar curvesGet 3 of 4 questions to level up!

## Calculator-active practice

Practice
Area with polar functions (calculator-active)Get 3 of 4 questions to level up!

#### Quiz 4

Level up on the above skills and collect up to 700 Mastery points
Up next for you:

#### Unit test

Level up on all the skills in this unit and collect up to 1500 Mastery points!

### About this unit

We are used to working with functions whose output is a single variable, and whose graph is defined with Cartesian, i.e., (x,y) coordinates. But there can be other functions! For example, vector-valued functions can have two variables or more as outputs! Polar functions are graphed using polar coordinates, i.e., they take an angle as an input and output a radius! Learn about these functions and how we apply the concepts of the derivative and the integral on them.