Practice converting between polar and rectangular coordinates, identifying polar graphs, testing symmetry, and analyzing common polar equations.
Read each problem carefully. Show your work in the space provided. Use exact values when possible.
Convert, interpret, and graph equations in polar form
Math - Grade 9-12
- 1
Convert the polar point (6, pi/6) to rectangular coordinates.
- 2
Convert the rectangular point (-3, 3sqrt(3)) to polar coordinates with r > 0 and 0 <= theta < 2pi.
- 3
Plot the polar point (4, 5pi/6). State the quadrant where the point lies.
- 4
Give two different polar coordinate pairs that represent the same point as (5, pi/4).
- 5
Convert the polar equation r = 8cos(theta) to rectangular form and describe its graph.
- 6
Convert the rectangular equation x^2 + y^2 = 6y to a polar equation.
- 7
Identify the graph of r = 3 + 3cos(theta). Name the type of limaçon and state its main direction.
- 8
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.
- 9
Find the maximum value of r for r = 4 + 2cos(theta), and state the angle where it occurs.
- 10
Determine the symmetry of r = 7sin(2theta). Test for symmetry about the polar axis, the line theta = pi/2, and the pole.
- 11
For the rose curve r = 5cos(3theta), state the number of petals and the length of each petal.
- 12
For the rose curve r = 4sin(6theta), state the number of petals and the length of each petal.
- 13
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)).
- 14
Find the area enclosed by one petal of r = 6sin(3theta).
- 15
A polar graph has equation r = 2theta for theta >= 0. Describe the graph and explain how r changes as theta increases.