Math: Precalculus: Polar Coordinates and Graphs

Convert the polar point (6, pi/6) to rectangular coordinates.

Convert the rectangular point (-3, 3sqrt(3)) to polar coordinates with r > 0 and 0 <= theta < 2pi.

Plot the polar point (4, 5pi/6). State the quadrant where the point lies.

Give two different polar coordinate pairs that represent the same point as (5, pi/4).

Convert the polar equation r = 8cos(theta) to rectangular form and describe its graph.

Convert the rectangular equation x^2 + y^2 = 6y to a polar equation.

Identify the graph of r = 3 + 3cos(theta). Name the type of limaçon and state its main direction.

For the polar equation r = 2 - 5sin(theta), identify whether the limaçon has an inner loop, a dimple, or no dimple. State its main direction.

Find the maximum value of r for r = 4 + 2cos(theta), and state the angle where it occurs.

Determine the symmetry of r = 7sin(2theta). Test for symmetry about the polar axis, the line theta = pi/2, and the pole.

For the rose curve r = 5cos(3theta), state the number of petals and the length of each petal.

For the rose curve r = 4sin(6theta), state the number of petals and the length of each petal.

Find the slope of the tangent line to r = 2cos(theta) at theta = pi/4. Use dy/dx = (r' sin(theta) + r cos(theta)) divided by (r' cos(theta) - r sin(theta)).

Find the area enclosed by one petal of r = 6sin(3theta).

A polar graph has equation r = 2theta for theta >= 0. Describe the graph and explain how r changes as theta increases.