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).

Tags

CCSS.HSN.CN.B.4

Front

How do you convert rectangular coordinates to polar coordinates?

Back

To convert rectangular coordinates (x, y) to polar coordinates (r, θ): 1. Calculate r = √(x² + y²). 2. Calculate θ = arctan(y/x) + π if x < 0.

Tags

CCSS.HSN.CN.B.4

Front

What is the significance of the angle in polar coordinates?

Back

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

Tags

CCSS.HSN.CN.B.4

Front

How do you find the rectangular coordinates from polar coordinates?

Back

To convert polar coordinates (r, θ) to rectangular coordinates (x, y): 1. x = r * cos(θ) 2. y = r * sin(θ)

Tags

CCSS.HSN.CN.B.4

Front

What does a negative radius in polar coordinates indicate?

Back

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

Tags

CCSS.HSN.CN.B.4

Front

Convert the polar point (3, π) to rectangular coordinates.

Back

(x, y) = (3 * cos(π), 3 * sin(π)) = (-3, 0).

Tags

CCSS.HSN.CN.B.4

Front

Convert the polar point (5, -rac{rac{3 ext{π}}{2}}) to rectangular coordinates.

Back

(x, y) = (5 * cos(-rac{3 ext{π}}{2}), 5 * sin(-rac{3 ext{π}}{2})) = (0, -5).

Tags

CCSS.HSN.CN.B.4

Front

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

Back

The polar coordinate is (4, rac{3 ext{π}}{2}).

Tags

CCSS.HSN.CN.B.4

Front

How do you determine the quadrant of a point in polar coordinates?

Back

The quadrant can be determined by the angle θ: 0 to rac{ ext{π}}{2} (Quadrant I), rac{ ext{π}}{2} to ext{π} (Quadrant II), ext{π} to rac{3 ext{π}}{2} (Quadrant III), rac{3 ext{π}}{2} to 2 ext{π} (Quadrant IV).

Tags

CCSS.HSN.CN.B.4

Front

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

Back

The polar coordinate is (4, 0).

Tags

CCSS.HSN.CN.B.4