Polar Graphs

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 (the polar axis). They are represented as (r, θ), where r is the radius and θ is the angle.

Front

How do you convert polar coordinates to rectangular coordinates?

Back

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

Front

What is the significance of the radius in polar coordinates?

Back

The radius (r) in polar coordinates represents the distance from the origin (pole) to the point. It is always a non-negative value.

Front

What does the angle represent in polar coordinates?

Back

The angle (θ) in polar coordinates represents the direction of the point from the origin, measured in radians or degrees from the positive x-axis (polar axis).

Front

Can polar coordinates represent the same point in multiple ways?

Back

Yes, polar coordinates can represent the same point in multiple ways. For example, (r, θ) and (r, θ + 2πk) for any integer k represent the same point.

Front

What is the polar coordinate for the point (0, -4) in rectangular coordinates?

Back

The polar coordinate for the point (0, -4) is (4, 3π/2).

Front

How do you write the ordered pair in polar coordinates?

Back

An ordered pair in polar coordinates is written as (r, θ), where r is the radius and θ is the angle.

Front

What is the polar coordinate for the point (3, 3π/4)?

Back

The polar coordinate (3, 3π/4) represents a point that is 3 units away from the origin at an angle of 3π/4 radians.

Front

True or False: The point (2, 7⁰) has a radius of 2.

Back

True. In the polar coordinate (2, 7⁰), the radius is 2.

Front

What is the rectangular coordinate of the polar point (4, 3π/2)?

Back

The rectangular coordinate of the polar point (4, 3π/2) is (0, -4).