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.

Tags

CCSS.HSN.CN.B.4

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.

Tags

CCSS.HSN.CN.B.4

Front

How do you convert polar coordinates to Cartesian coordinates?

Back

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

Tags

CCSS.HSN.CN.B.4

Front

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

Back

Tags

CCSS.HSN.CN.B.6

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.

Tags

CCSS.HSN.CN.B.4

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.

Tags

CCSS.HSN.CN.B.4

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.

Tags

CCSS.HSN.CN.B.4

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).

Tags

CCSS.HSN.CN.B.4

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.

Tags

CCSS.HSN.CN.B.4

Front

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

Back

The polar coordinate is (√2, π/4).

Tags

CCSS.HSN.CN.B.4