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Find the polar coordinates of the point (7, -7)?

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Please explain/show how you got the answer. Thanks :)

asked May 30, 2013 in ALGEBRA 2 by dkinz Apprentice

1 Answer

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The coordinates (x , y) = (7, -7)

The polar coordinates (rcosθ , rsinθ)

r2 = x2 + y2 = 72 + (-7)2 = 98

Take square root to each side

r = √x2 + y2 = √98

tanθ = y / x

θ = arctan(y / x) = arctan(-7 / 7) = arctan(-1) = 3π/4,7π/4

Substitute r = √98 and θ = 3π/4,7π/4

The polar coordinates are (√98cos3π/4   , √98sin3π/4) and (√98cos7π/4   , √98sin7π/4).

 

answered May 30, 2013 by diane Scholar

The rectanglular coordinate point : (x, y)

The polar coordinate point : (r, θ) = [ √(x2 + y2), tan-1(y/x) ].

Since x = r cos(θ), y = r sin(θ) and tan(θ) = y/x.

r = √(x2 + y2) = √[ (7)2 + (- 7)2 ] = √[49 + 49) = 7√2.

θ = tan-1[ (- 7)/(7) ] = tan-1(- 1) = - tan-1(1) = - π/4.

The polar form of (7, - 7) is (r, θ) = (7√2, - π/4).

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