Question

Write the rectangular point (-4,-8) in polar coordinates. Give your answer to two decimal places.

Answer 1

Rectangular coordinate=(-4,-8)

it means x=-4 and y=-8

now for polar coordinate

r=√(x^2+y^2)=√[(-4)^2+(-8)^2]=√(16+64)=√80=8.94

and tan(theta)=y/x=-8/-4=2

theta=arctan (2)=63.43°

also, tan is positive in third quadrant

so, theta=180°+63.43°=243.43°

and our point is in third quadrant also, therefore correct angle is 243.43°

hence, polar coordinates of the given rectangular coordinate (-4,-8) is (8.94,243.43°)