Polar Coordinates I

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 formula is: x = r * cos(θ), y = r * sin(θ), where r is the radius and θ is the angle.

Front

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

Back

The formula is: r = √(x² + y²), θ = arctan(y/x).

Front

What does the variable 'r' represent in polar coordinates?

Back

'r' represents the distance from the origin to the point.

Front

What does the variable 'θ' represent in polar coordinates?

Back

'θ' represents the angle measured from the positive x-axis.

Front

How do you determine the angle θ in polar coordinates?

Back

The angle θ can be determined using the arctangent function: θ = arctan(y/x).

Front

What is the range of the angle θ in polar coordinates?

Back

The angle θ is typically measured in degrees or radians and can range from 0° to 360° (or 0 to 2π radians).

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 coordinate (r, θ).

Front

What is the significance of the angle in polar coordinates?

Back

The angle indicates the direction of the point from the origin.

Front

How do you plot a point given in polar coordinates?

Back

To plot a point (r, θ), measure the angle θ from the positive x-axis and then move r units away from the origin in that direction.