3.13 - 3.14 AP Precalc Review

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 rectangular coordinates to polar coordinates?

Back

To convert from rectangular coordinates (x, y) to polar coordinates (r, θ): 1. Calculate r = √(x² + y²). 2. Calculate θ = arctan(y/x) (considering the quadrant).

Front

What is the polar coordinate of the point (-3, 0)?

Back

The polar coordinate of the point (-3, 0) is (3, π).

Front

What is the general form of a polar equation?

Back

A polar equation is typically expressed as r = f(θ), where r is the distance from the origin and θ is the angle.

Front

What does the equation r = 2 + 3 cos(θ) represent?

Back

This equation represents a limaçon with an inner loop.

Front

How do you identify the graph of a polar equation?

Back

To identify the graph of a polar equation, analyze the equation's form, identify key features (like symmetry and intercepts), and plot points for various values of 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 is the polar coordinate representation of the point (-4, -2π/3)?

Back

The polar coordinate representation of the point (-4, -2π/3) is (4, π/3).

Front

What is the relationship between polar and rectangular coordinates?

Back

The relationship is given by: x = r cos(θ) and y = r sin(θ).

Front

What is a limaçon?

Back

A limaçon is a type of polar curve that can have an inner loop, be dimpled, or be convex, depending on the parameters in the equation.