Parametric Equations and 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,) .

Solution for Problem 1 >>

(r, θ) = (2,),(- 2,) .

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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) .

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) .

Solution for Problem 3 >>

(r, θ) = (,),(- ,) .

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

Solution for Problem 4 >>

(x, y) = (,) .

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

Solution for Problem 5 >>

(x, y) = (- ,) .

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

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

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