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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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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!
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!
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!
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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 concepts of the derivative and the integral on them.AP® is a registered trademark of the College Board, which has not reviewed this resource.