A circle in the Cartesian plane is given by the equation

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

x^{2}+y^{2}=5y

. In this problem you will express the circle in polar form and interpret the result. (a) Rewrite the given Cartesian equation in polar coordinates by substituting

x=r\cos\theta

and

y=r\sin\theta

. Simplify your answer so that

r

is explicitly expressed as a function of

\theta

. (b) Determine all values of

\theta

for which the corresponding

r

obtained in Part (a) is non-negative. Provide a complete algebraic justification. (c) Describe, in words, how the restriction on

\theta

found in Part (b) relates to the location of the circle in the Cartesian plane.

Related theory

Polar Coordinates
Trigonometric Functions

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