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

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Possible mastery points

Arc length: parametric curves

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Planar motion

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Quiz 1

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

Area: polar regions (single curve)

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Area: polar regions (two curves)

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Arc length: polar curves

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Calculator-active practice

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Quiz 2

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

Level up on all the skills in this unit and collect up to 700 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 concept of the integral on them.