find polar coordinates

Question

(-5,-5√3); r≤0 and -pi≤∅≤pi

Answer 1

the underlying formula that you want to use to convert these over are

r = +/- sqrt(x^2 + y^2)

tan(theta) = y / x

for this set of parameters that means taking

r = sqrt((-5)^2) + (-5*sqrt(3)^2)

r = +/- 10

tan(theta) = y/x = sqrt(3)

theta = pi/3 +/- pi

then based on the other constraints it would be

(-10, pi/3) since we need r to be negative