Polar Review 3-4

Front

What is the polar coordinate system?

Back

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

Front

What is the relationship between polar and rectangular coordinates?

Back

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

Front

How do you convert rectangular coordinates to polar coordinates?

Back

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

Front

What is the formula for converting polar coordinates to rectangular coordinates?

Back

To convert (r, θ) to rectangular coordinates (x, y): x = r * cos(θ) and y = r * sin(θ).

Front

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

Back

The distance from the origin to the point.

Front

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

Back

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

Front

How do you find the angle θ in polar coordinates when given rectangular coordinates?

Back

Use θ = arctan(y/x), adjusting for the quadrant of the point.

Front

What is the polar coordinate for the point (0, 0) in rectangular coordinates?

Back

(0, θ) for any angle θ, since the distance from the origin is zero.

Front

What is the significance of the angle being measured in radians or degrees in polar coordinates?

Back

It determines the direction of the point in relation to the positive x-axis.

Front

How do you convert the polar coordinate (5, 50°) to rectangular coordinates?

Back

x = 5 * cos(50°), y = 5 * sin(50°) which results in approximately (3.2, 3.8).