Rectangular Coordinates to Polar Coordinates?

Question

Let the letters x and y represent rectangular coordinates. Write an equation using polar coordinates (r, theta).

HINT IN THE BOOK

Use the following equations accordingly for each question as needed:

x = rcos(theta)

y = rsin(theta)

r^2 = x^2 + y^2

tan(theta) = y/x, where x does not equal zero.

(1) 4x^2(y) = 1

(2) y = - 3

Answer 1

(1) 4x²y = 4r²cos(theta) * rsin(theta)
= 4r³ cos(theta)sin(theta) = 1
or 2r³sin(2 theta) = 1

(2) rsin(theta) = -3