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

AP Calc:

CHA (BI)

, CHA‑3 (EU)

, CHA‑5 (EU)

, CHA‑6 (EU)

, FUN (BI)

, FUN‑3 (EU)

, FUN‑8 (EU)

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### About this unit

While we're often familiar with functions that output just one variable and are graphed with Cartesian coordinates, there are other possibilities! Vector-valued functions, for example, can output multiple variables. Polar functions, too, differ, using polar coordinates for graphing. We can still explore these functions with derivatives and integrals.AP Calc:

CHA (BI)

, CHA‑3 (EU)

, CHA‑3.G (LO)

, CHA‑3.G.1 (EK)

### Practice

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

AP Calc:

CHA (BI)

, CHA‑3 (EU)

, CHA‑3.G (LO)

, CHA‑3.G.3 (EK)

### Practice

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

AP Calc:

CHA (BI)

, CHA‑6 (EU)

, CHA‑6.B (LO)

, CHA‑6.B.1 (EK)

### Learn

### Practice

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

Level up on the above skills and collect up to 240 Mastery points

AP Calc:

CHA (BI)

, CHA‑3 (EU)

, CHA‑3.H (LO)

, CHA‑3.H.1 (EK)

### Learn

### 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!

AP Calc:

FUN (BI)

, FUN‑8 (EU)

, FUN‑8.B (LO)

, FUN‑8.B.1 (EK)

, FUN‑8.B.2 (EK)

### Learn

### 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!

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

AP Calc:

FUN (BI)

, FUN‑3 (EU)

, FUN‑3.G (LO)

, FUN‑3.G.1 (EK)

, FUN‑3.G.2 (EK)

### Learn

### Practice

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

AP Calc:

CHA (BI)

, CHA‑5 (EU)

, CHA‑5.D (LO)

, CHA‑5.D.1 (EK)

, CHA‑5.D.2 (EK)

### 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!

AP Calc:

CHA (BI)

, CHA‑5 (EU)

, CHA‑5.D (LO)

, CHA‑5.D.1 (EK)

, CHA‑5.D.2 (EK)

### Practice

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

AP Calc:

CHA (BI)

, CHA‑5 (EU)

, CHA‑5.D (LO)

, CHA‑5.D.1 (EK)

, CHA‑5.D.2 (EK)

### 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 480 Mastery points

Up next for you:

Level up on all the skills in this unit and collect up to 1400 Mastery points!#### Unit test

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