Polar Coordinates II

Front

What are polar coordinates?

Back

Polar coordinates are a two-dimensional coordinate system where each point is determined by a distance from a reference point (the origin) and an angle from a reference direction.

Front

What is the formula to convert polar coordinates to Cartesian coordinates?

Back

The conversion formulas are: x = r * cos(θ) and y = r * sin(θ), where (r, θ) are the polar coordinates.

Front

What is the angle θ in polar coordinates?

Back

The angle θ is the counterclockwise angle measured from the positive x-axis to the line connecting the origin to the point.

Front

What does the variable r represent in polar coordinates?

Back

The variable r represents the radial distance from the origin to the point in the polar coordinate system.

Front

How do you find the distance from the origin in polar coordinates?

Back

The distance from the origin is given by the value of r in the polar coordinates (r, θ).

Front

What is the polar coordinate representation of the point (1, 45°)?

Back

In polar coordinates, the point (1, 45°) means the point is 1 unit away from the origin at an angle of 45 degrees.

Front

How do you determine the angle θ for a point in polar coordinates?

Back

To determine θ, you can use the arctangent function: θ = arctan(y/x) for Cartesian coordinates (x, y).

Front

What is the relationship between polar coordinates and trigonometric functions?

Back

Polar coordinates utilize trigonometric functions to relate the angle θ and the radial distance r to the Cartesian coordinates.

Front

What is the significance of negative values of r in polar coordinates?

Back

Negative values of r indicate that the point is in the opposite direction of the angle θ.

Front

How do you express the point (2, 210°) in Cartesian coordinates?

Back

Using the conversion formulas: x = 2 * cos(210°) and y = 2 * sin(210°), the Cartesian coordinates are (-1.732, -1).