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

This course is a part of
**AP®︎ Calculus BC**, a 12-course Topic series from Khan Academy.

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.

This course contains 9 segments:

**Defining and differentiating parametric equations**

**Second derivatives of parametric equations**

**Finding arc lengths of curves given by parametric equations**

**Defining and differentiating vector-valued functions**

**Solving motion problems using parametric and vector-valued functions**

**Defining polar coordinates and differentiating in polar form**

**Finding the area of a polar region or the area bounded by a single polar curve**

**Finding the area of the region bounded by two polar curves**

**Calculator-active practice**

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Rating | Not enough ratings |
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Length | 9 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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Rating | Not enough ratings |
---|---|

Length | 9 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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