Question

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

Answer 1

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°).

Answer 2

Since the point lies of the negative side of the x axis, it forms an angle of 180° with the positive direction of the x axis.

So, if we start from (1,0), a rotation of 180° will bring us to (-1,0). If we scale the point with factor 3, we have (-3,0).

So, the polar coordinates are (3, 180°)