Graphing Points in Polar

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).

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 angle in polar coordinates?

Back

The angle in polar coordinates determines the direction of the point from the origin, measured counterclockwise from the positive x-axis.

Front

What does a negative radius indicate in polar coordinates?

Back

A negative radius indicates that the point is in the opposite direction of the angle specified.

Front

How can the same point in polar coordinates be represented in different ways?

Back

A point (r, θ) can also be represented as (-r, θ + π) or (r, θ + 2kπ) for any integer k.

Front

What is the polar coordinate for the point at (0, 0)?

Back

The polar coordinate for the origin is (0, θ) for any angle θ.

Front

How do you find the angle for a given point in polar coordinates?

Back

The angle θ can be found using the arctangent function: θ = arctan(y/x) for rectangular coordinates (x, y).

Front

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

Back

The polar coordinate for the point (4, 0) is (4, 0°) or (4, 0 radians).

Front

How do you determine if a point lies on a polar curve?

Back

To determine if a point lies on a polar curve defined by θ = f(r), substitute the point's polar coordinates into the equation and check if it holds true.

Front

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

Back

The polar coordinate for the point (-4, 0) is (4, 180°) or (4, π radians).