Cartesian to Polar Equations


Replace the Cartesian equations in Exercises 53–66 with equivalent polar equations.


x - y = 3

Cartesian to Polar Coordinates

Find the polar coordinates, 0 ≤ θ < 2π and r ≥ 0, of the following points given in Cartesian coordinates.

b. (-3,0)

Cartesian to Polar Coordinates

Find the polar coordinates, 0 ≤ θ ≤ 2π and r ≤ 0, of the following points given in Cartesian coordinates.

c. (−1, √3)

Polar to Cartesian Equations

Replace the polar equations in Exercises 27–52 with equivalent Cartesian equations. Then describe or identify the graph.

r² = 4r sin θ

Polar to Cartesian Equations

Replace the polar equations in Exercises 27–52 with equivalent Cartesian equations. Then describe or identify the graph.

r = 3 cos θ

Cartesian to Polar Equations

Replace the Cartesian equations in Exercises 53–66 with equivalent polar equations.

(x + 2)² + (y − 5)² = 16"

Polar Coordinates

Exercises 19–22 give the eccentricities of conic sections with one focus at the origin of the polar coordinate plane, along with the directrix for that focus. Find a polar equation for each conic section.

e = 1/3, r sin θ = −6

Graphing Sets of Polar Coordinate Points

Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises 11–26.

θ = π/2, r ≥ 0

Symmetries and Polar Graphs

Identify the symmetries of the curves in Exercises 1–12. Then sketch the curves in the xy-plane.

r = 1 + 2 sin θ