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Parametric Equations and Polar Coordinates

Problems

Polar Coordinates

Graphing in Polar Coordinates

Problem : Given a point in rectangular coordinates (x, y) , express it in polar coordinates (r, θ) two different ways such that 0≤θ < 2Π : (x, y) = (1,) .

(r, θ) = (2,),(- 2,) .

Problem : Given a point in rectangular coordinates (x, y) , express it in polar coordinates (r, θ) two different ways such that 0≤θ < 2Π : (x, y) = (- 4, 0) .

(r, θ) = (4, Π),(- 4, 0) .

Problem : Given a point in rectangular coordinates (x, y) , express it in polar coordinates (r, θ) two different ways such that 0≤θ < 2Π : (x, y) = (- 7, - 7) .

(r, θ) = (,),(- ,) .

Problem : Given a point in polar coordinates (r, θ) , express it in rectangular coordinates (x, y) : (r, θ) = (3,) .

(x, y) = (,) .

Problem : Given a point in polar coordinates (r, θ) , express it in rectangular coordinates (x, y) : (r, θ) = (1,) .

(x, y) = (- ,) .

Problem : Given a point in polar coordinates (r, θ) , express it in rectangular coordinates (x, y) : (r, θ) = (0,) .

(x, y) = (0, 0) .

Problem : How many different ways can a point be expressed in polar coordinates such that r > 0 ?

An infinite number. (r, θ) = (r, θ +2) , where n is an integer.

Problem : How many different ways can a point be expressed in polar coordinates such that 0≤θ < 2 ?

2n . In every cycle of 2Π , there are two pairs of polar coordinates, (r, θ) and (- r, θ + (2n + 1)Π) for every point.

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