Polar to Cartesian Equations


Sketch the lines in Exercises 23-28. Also, find a Cartesian equation for each line.


r cos (θ − 3π/4) = (√2)/2

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

Lines

Sketch the lines in Exercises 45–48 and find Cartesian equations for them.

r cos (θ + π/3) = 2

Circles

Sketch the circles in Exercises 53–56. Give polar coordinates for their centers and identify their radii.

r = −2 cos θ

Examples of Polar Equations

[Technology Exercise] Graph the lines and conic sections in Exercises 65–74.

r = −2 cos θ

Cartesian to Polar Equations

Find polar equations for the circles in Exercises 33–36. Sketch each circle in the coordinate plane and label it with both its Cartesian and polar equations.

x² + y² + 5y = 0

Plot the point on the polar coordinate system.

$(5,210°)$

Plot the point on the polar coordinate system.

$(-3,-90°)$

Plot the point on the polar coordinate system.

$(6,-\(\frac{11\pi}{6}\))$