find polar coordinates

Question

(4√3,4); r≤0 and 0≤∅≤2pi

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(4(sqrt(3)^2) + 4^2)

r = +/- 8

tan(theta) = y/x = 1/sqrt(3)

theta = 30 +/- pi

then based on the other constraints it would be

(-8, 7pi/6) since we need r to be negative