Question

Convert the Cartesian coordinates (2, -2) to polar coordinates. (2√2, 315°) (2√2, 330°) (2√2, 345°)

Answer 1

(2√2, 315°)

Explanation:

Answer 2

Convert the Cartesian coordinates (2, -2) to polar coordinates. (2√2, 315°) (2√2, 330°) (2√2, 345°)

To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

r = √ ( x² + y² )

θ = arctan ( y / x )

r = √ [ 2² + (-2)² ] = √8 = 2√2

θ = arctan ( y / x ) = arctan (-2/2)

θ = arctan (-1) = n180º + 135º = nπ + 3π/4 => n=0, +-1, +-2, +-3...

So, a principal value of arctan(-1) in [0, π] is 3π/4 = 135º

There is another in [0, 2π] => 1π + 3π/4 = 7π/4 = 180º + 135º = 315º

Answer : (2√2, 315°)

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