Plotting Polar Points - day 1

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 (usually the positive x-axis).

Front

How do you convert Cartesian coordinates (x, y) to polar coordinates (r, θ)?

Back

To convert Cartesian coordinates to polar coordinates, use the formulas: r = √(x² + y²) and θ = arctan(y/x).

Front

What is the significance of the radius (r) in polar coordinates?

Back

The radius (r) represents the distance from the origin to the point in the polar coordinate system.

Front

What does the angle (θ) represent in polar coordinates?

Back

The angle (θ) represents the direction of the point from the origin, measured counterclockwise from the positive x-axis.

Front

How do you plot a point given in polar coordinates (r, θ)?

Back

To plot a point in polar coordinates, measure the angle θ from the positive x-axis, then move r units from the origin in that direction.

Front

What is the relationship between polar coordinates and Cartesian coordinates?

Back

Polar coordinates (r, θ) can be converted to Cartesian coordinates (x, y) using the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

What is the polar coordinate of the point (0, 0) in Cartesian coordinates?

Back

The polar coordinate of the point (0, 0) is (0, θ) for any angle θ, since it is at the origin.

Front

How do you express negative angles in polar coordinates?

Back

Negative angles in polar coordinates indicate a clockwise rotation from the positive x-axis. For example, -π/4 is equivalent to 7π/4.

Front

What is the polar coordinate of the point (4, -π/4)?

Back

The polar coordinate (4, -π/4) indicates a point that is 4 units away from the origin at an angle of -π/4 radians.

Front

How do you determine the quadrant of a point given in polar coordinates?

Back

The quadrant can be determined by the angle θ: 0 to π/2 (1st quadrant), π/2 to π (2nd quadrant), π to 3π/2 (3rd quadrant), and 3π/2 to 2π (4th quadrant).