Determine two pairs of polar coordinates for (-3,0) when 0°< <360°

The given point is:

(x, y) = (-3, 0)

First, we find  r using:

r√ x ^2  +  y ^2  = √ ( − 3 ) ^2  +  0 ^2  =  3

Now we will find a using:

a = tan^-1 ∣ y /x ∣

= tan^-1  ∣ 0/-3∣

= tan^-1 0

= 0                             [ ∵ tan  0  =  0 ]

We know that (-3, 0) is in quadrant II.

so the angle is θ  =  180  −  α  =  180  −  0  =  180 °

Therefore, the corresponding polar coordinates are (r, θ ) = (3, 180°).