Understanding Polar Coordinates

Polar coordinates use radius and angle, while Cartesian uses x and y.

Polar coordinates use x and y, while Cartesian uses radius and angle.

Polar coordinates are only used in 3D space.

Cartesian coordinates are only used in 3D space.

x = R * cos(theta)

x = R * sin(theta)

x = R * tan(theta)

x = R / cos(theta)

The conversion of x-coordinate from polar to Cartesian.

The Pythagorean theorem in Cartesian coordinates.

The relationship between radius and angle in polar coordinates.

The conversion of y-coordinate from polar to Cartesian.

Plot it in the opposite quadrant.

Use the absolute value of the radius.

Reflect the point across the origin.

Ignore the negative sign and plot as positive.

Polar coordinates are only used in physics.

Polar coordinates are only used for circular shapes.

Polar coordinates can have multiple representations for the same point.

Polar coordinates have unique representations for each point.

Use the formulas x = R * cos(theta) and y = R * sin(theta).

Use the formulas R = sqrt(x^2 + y^2) and theta = tan^-1(y/x).

Use the formulas R = x + y and theta = x - y.

Use the formulas R = x^2 + y^2 and theta = x/y.

R = 2, theta = 4PI/3

R = 2, theta = PI/3

R = sqrt(3), theta = PI/3

R = sqrt(3), theta = 4PI/3

An annular ring

A triangle

A square

A circle

It has no effect on the graph.

It changes the region to a square.

It doubles the size of the region.

It reflects the region across the origin.

A rectangle

An hourglass shape

A circular arc

A straight line