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# Unit 4: Parametric equations, polar coordinates, and vector-valued functions

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## 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 concept of the integral on them.### Learn

### Practice

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

### Practice

- Planar motion (with integrals)Get 3 of 4 questions to level up!

Level up on the above skills and collect up to 160 Mastery points

### Learn

### 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!

### Practice

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

### Learn

### Practice

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

### Practice

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

Level up on the above skills and collect up to 400 Mastery points

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Level up on all the skills in this unit and collect up to 700 Mastery points!