Polar Coordinate System: Video e Problemi di Pratica

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 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)

Transform the given rectangular equation into a polar equation.

5x + 2y = 9

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)

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.

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)

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 = 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

The point $(6,\frac{5\pi }{6})$ is given in polar coordinates. Find its rectangular $x$-coordinate.

The point $(-5,\frac{\pi }{4})$ is rewritten as an equivalent polar coordinate with positive radius and angle $\theta$ in the interval . Find $\theta$.