Polar Coordinate System Practice Problems

Transform the given rectangular equation into a polar equation.

5x + 2y = 9

Transform the given rectangular equation into a polar equation.

x = 12

Transform the given rectangular equation into a polar equation.

x² + y² = 361

Transform the given rectangular equation into a polar equation.

(x - 5)² + y² =25

Transform the given polar equation into a rectangular equation. Use the resulting equation to draw the graph.

r = 4

Transform the given polar equation into a rectangular equation. Use the resulting equation to draw the graph.

r = 2 csc θ

Transform the given polar equation into a rectangular equation. Use the resulting equation to draw the graph.

r = 8 cos θ

Transform the given polar equation into a rectangular equation. Use the resulting equation to draw the graph.

r = 8 cos θ + 10 sin θ

Transform the given polar equation into a rectangular equation. Find the slope and the y-intercept of the resulting equation.

r sin (θ − π/3) = 4

Convert the given coordinates into rectangular coordinates. Find the distance between the resulting points.

(4, 3π/4) and (8, π/4)

Which of the following polar coordinates represents the same location as (4, 80°)?

I. (4, 440°)

II. (-4, 260°)

III. (-4, 300°)

IV. (-4, -100°)

Which of the following polar coordinates represents the same location as (8, 210°)?

I. (8, 390°)

II. (-8, 50°)

III. (8, 410°)

IV. (-8, 30°)

Which of the following polar coordinates represents the same location as (5, -5π/4)?

I. (5, 3π/4)

II. (5, π/6)

III. (-5, -9π/4)

IV. (-5, -2π)

Which of the following polar coordinates represents the same location as (-6, 2π/3)?

I. (-6, 4π/3)

II. (-6, 11π/3)

III. (6, 11π/3)

IV. (6, -π/3)

Which of the following polar coordinates represents the same location as (-10, -π/6)?

I. (10, 17π/6)

II. (-10, 15π/6)

III. (10, 13π/6)

IV. (-10, 11π/6)

Which of the following polar coordinates represents the same location as (-15, 5π)?

I. (-15, 8π)

II. (-15, -π)

III. (15, 8π)

IV. (15, 4π)

Convert the following polar coordinates to rectangular coordinates:

(15, 270°)

Convert the following polar coordinates to rectangular coordinates:

(-12, 3π/2)

Convert the following polar coordinates to rectangular coordinates:

(13.4, 5.3)

Convert the following rectangular coordinates to polar coordinates. Write the angle in radians:

(-8, 8)

Convert the following rectangular coordinates to polar coordinates. Write the angle in radians:

(21, -7√3)

Consider the following equation.

r = 10 + 7 cos θ

Perform the test for symmetry with respect to the polar axis, the line θ = π/2, and the pole.

Convert the following rectangular coordinates to polar coordinates. Write the angle in radians:

(-10, -10√3)

Convert the following rectangular coordinates to polar coordinates. Write the angle in radians:

(0, 13)

The following point has polar coordinates. Plot it in a polar coordinate system. Then, determine another point that has the same location as the given in which r > 0 and 4π < θ < 6π:

(7, π/3)

The following point has polar coordinates. Plot it in a polar coordinate system. Then, determine another point that has the same location as the given in which r < 0 and 0 < θ < 2π:

(9, 3π/2)

Plot the provided complex number using the formula e^iθ = cos θ + i sin θ.

e^(π/12)i

Plot the provided complex number using the formula e^iθ = cos θ + i sin θ.

-e^5πi

Identify the point on the graph corresponding to the provided polar coordinates, with points P, Q, R, and S indicated. 

(2, 135°)

Identify the point on the graph corresponding to the provided polar coordinates, with points P, Q, R, and S indicated. 

(-4, 5π/4) 

Identify the point on the graph corresponding to the provided polar coordinates, with points P, Q, R, and S indicated.

(4, π) 

Identify the point on the graph corresponding to the provided polar coordinates, with points P, Q, R, and S indicated.

(2, -45°) 

Identify the point on the graph corresponding to the provided polar coordinates, with points P, Q, R, and S indicated.

(-4, -3π/4) 

Represent the solutions in polar and rectangular form after solving the given equation in the complex number system. 

x⁶ -64 = 0

Represent the solutions in polar and rectangular form after solving the given equation in the complex number system. 

x⁴ +625i = 0

Represent the solutions in polar and rectangular form after solving the given equation in the complex number system. 

x³ -(1 +i) = 0

Plot the given polar coordinates on a polar coordinate system. 

(5, 60°)

Plot the given polar coordinates on a polar coordinate system. 

(9, 90°)

Plot the given polar coordinates on a polar coordinate system. 

(20, 5π/4)

Plot the given polar coordinates on a polar coordinate system. 

(-15, π)

Plot the given polar coordinates on a polar coordinate system. 

(-6, -2π/3)

Test the polar equation for symmetry and sketch its graph: 

r = 12 +12 sin θ 

Test the polar equation for symmetry and sketch its graph: 

r = 13 + cos θ 

For the given equation (x +11)² +y² = 121, convert it to a polar equation. 

Sketch the given polar equation in the polar coordinate system. 

r = 5 +cos θ

Test the polar equation for symmetry and sketch its graph:

r = 3/(3 - cos θ)

Test the polar equation for symmetry and sketch its graph:

r = 7 + 5 sin 2θ

Convert the given polar equation to a rectangular equation and plot the polar equation using the knowledge of rectangular equation.

θ = 5π/6

Convert the given polar equation to a rectangular equation and plot the polar equation using the knowledge of rectangular equation.

r = 8 csc θ

Consider the following equation.

r = 9 + 5 cos θ

Perform the test for symmetry with respect to the polar axis, the line θ = π/2, and the pole.

Test the polar equation for symmetry and sketch its graph:

r = 8 cos θ

Test the polar equation for symmetry and sketch its graph:

r = 6 - 6 sin θ

Test the polar equation for symmetry and sketch its graph:

r = 8 + 8 cos θ

Test the polar equation for symmetry and sketch its graph:

r = 9 + (9/2)cos θ

Test the polar equation for symmetry and sketch its graph:

r = 5 + 11 cos θ

Test the polar equation for symmetry and sketch its graph:

r = 4 - 7 sin θ

Test the polar equation for symmetry and sketch its graph:

r = (7/2) sin 3θ

Test the polar equation for symmetry and sketch its graph:

r = 5 - 11 sin θ

Test the polar equation for symmetry and sketch its graph:

r cos θ = - 7

Test the polar equation for symmetry and sketch its graph:

r = 4 cos (θ/2)