Question

Find polar coordinates of the point whose cartesian coordinates are given. (-2√3 , 2)

Answer 1

The  polar coordinates of the point whose cartesian coordinates is (-2√3 , 2) is (4cos210, 4sin210)

Polar form of a rectangular coordinate

The polar form of a rectangular coordinate (x, y) is expressed as (rcos theta, r sin theta)

Given the coordinate (-2√3 , 2)

r = √(-2√3)²+2²

r = √12+4

r = 4

theta = tan^-1(-2/2√3)

theta = tan^-1(-1/√3)

theta = -30 degrees = 210 degrees

The  polar coordinates of the point whose cartesian coordinates is (-2√3 , 2) is (4cos210, 4sin210)

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