Polar Coordinates

Front

What does the first number in polar coordinates (r, θ) represent?

Back

The first number, r, represents the radius or distance from the origin.

Front

What does the second number in polar coordinates (r, θ) represent?

Back

The second number, θ, represents the angle measured from the positive x-axis.

Front

How do you convert polar coordinates to Cartesian coordinates?

Back

Use the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

What is the distance formula for two points in polar coordinates (r1, θ1) and (r2, θ2)?

Back

Front

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

Back

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

Front

How can you represent the same point in polar coordinates using different angles?

Back

You can add or subtract multiples of 2π to the angle θ, e.g., (r, θ + 2kπ) where k is an integer.

Front

What is the significance of negative radius in polar coordinates?

Back

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

Front

How do you graph the point (-2, 3π/2) in polar coordinates?

Back

Move 2 units in the direction opposite to 3π/2 (which points downwards) to reach the point (2, π/2).

Front

Which of the following polar coordinates represents the same point as (4, π/3)? (4, -5π/3), (4, 5π/3), (-4, 5π/3), (-4, -2π/3)

Back

(4, -5π/3), (4, 5π/3) represent the same point.

Front

What is the polar coordinate for the point (1, 1) in Cartesian coordinates?

Back

The polar coordinate is (√2, π/4).