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°)
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°).
