The polar coordinate of a point is in the form of:
polar coordinate: (r, θ)
where r is the resultant vector and θ is the angle from the x axis to the vector
We can solve for r using the hypotenuse formula:
r^2 = x^2 + y^2
r^2 = (- 4)^2 + (3)^2
r^2 = 16 + 9
r^2 = 25
r = ± 5
Using the tan function to find for θ:
tan θ = y / x
θ = tan^-1 (3 / -4)
θ = -36.8699 (clockwise from x axis) or equivalent to θ = 360-36.8699 = 323.1301°
Since our other point lies on the 3rd quadrant (negative x, positive y) we add 180° to get the other angle:
θ = 180 – 36.8699
θ = 143.1301° (counterclockwise from x-axis)
Therefore the 2 sets of polar coordinates are:
(5, 323.1301°) and (-5, 143.1301°)
or in rad form:
(5, 1.8π) and (-5, 0.8π)
