Polar Coordinates and 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).

Tags

CCSS.HSN.CN.B.4

Front

How do you convert polar coordinates (r, θ) to rectangular coordinates (x, y)?

Back

The conversion formulas are: x = r * cos(θ) and y = r * sin(θ).

Tags

CCSS.HSN.CN.B.4

Front

What is the ordered pair in polar coordinates?

Back

The ordered pair in polar coordinates is written as (r, θ).

Tags

CCSS.HSN.CN.B.4

Front

What is the polar equation of a circle with radius 3 centered at the origin?

Back

The polar equation is r = 3.

Tags

CCSS.HSN.CN.B.4

Front

What is a cardioid in polar coordinates?

Back

A cardioid is a heart-shaped curve represented by the polar equation r = a + b * sin(θ) or r = a + b * cos(θ), where a and b are constants.

Front

How do you find the area enclosed by a polar curve?

Back

The area A enclosed by a polar curve r = f(θ) from θ = a to θ = b is given by the formula: A = 1/2 * ∫[a to b] (f(θ))^2 dθ.

Front

What is the significance of the angle θ in polar coordinates?

Back

The angle θ represents the direction of the point from the origin, measured counterclockwise from the positive x-axis.

Tags

CCSS.HSN.CN.B.4

Front

What is the polar equation for a limacon with an inner loop?

Back

The polar equation for a limacon with an inner loop is of the form r = a + b * sin(θ) or r = a + b * cos(θ) where |b| > |a|.

Front

How do you graph polar coordinates?

Back

To graph polar coordinates, plot the point at a distance r from the origin at an angle θ from the polar axis.

Tags

CCSS.HSN.CN.B.4

Front

What is the relationship between polar and rectangular coordinates?

Back

The relationship is defined by the equations: x = r * cos(θ) and y = r * sin(θ), and the inverse is r = √(x^2 + y^2) and θ = tan^(-1)(y/x).

Tags

CCSS.HSN.CN.B.4