Convert the rectangular coordinates into polar coordinates.?

Question

(-8 , i√ 3)?

Answer 1

The point is (-8, i√3).

The rectangular coordinate point : (x, y) = (-8, √3).

The point (-8, √3) lies in second quadrant.

tan θ = y/x = √3/(-8) = - √3/8 = - 0.2165.

θ = tan^-1 (-0.2165) = - 12.21^o.

The value of tan θ is negative in second and fourth quadrant.

In second quadrant, the angle θ = 167.78^o.

In fourth quadrant, the angle θ = 347.78^o.

r² = (x² + y²) = (-8)² + (√3)² = 64 + 3 = 67.

r = ± √(67).

Because θ was chosen to be in the same quadrant (fourth) as (x, y), we should be use a positive value of r.

The polar coordinates points is (√67, 167.78^o).

Because θ was not chosen to be in the same quadrant (second) as (x, y), we should be use a negative value of r.

The polar coordinates points is (-√67, 347.78^o).

The polar coordinates points are (√67, 167.78^o) and (-√67, 347.78^o).