Polar Coordinates III

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 pole) and an angle from a reference 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 does the angle θ represent in polar coordinates?

Back

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

Front

What does the radius r represent in polar coordinates?

Back

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

Front

How do you find the radius r for a given angle θ in polar coordinates?

Back

The radius r can be determined based on the specific problem or context, often given in the problem statement.

Front

If θ = 0°, what is the position of the point in polar coordinates?

Back

If θ = 0°, the point lies on the positive x-axis at a distance r from the origin.

Front

If θ = 90°, what is the position of the point in polar coordinates?

Back

If θ = 90°, the point lies on the positive y-axis at a distance r from the origin.

Front

What is the value of r when θ = 75° in the given problem?

Back

The value of r when θ = 75° is 3.

Front

What is the value of r when θ = 45° in the given problem?

Back

The value of r when θ = 45° is 1.

Front

What is the value of r when θ = 90° in the given problem?

Back

The value of r when θ = 90° is 4.