FLASHCARD for MAJOR GRADE - Polar Coordinates and Equations

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 Cartesian coordinates (x, y) to Polar coordinates (r, θ)?

Back

To convert from Cartesian to Polar coordinates, use the formulas: r = √(x² + y²) and θ = arctan(y/x).

Front

What is the formula for converting Polar coordinates (r, θ) to Cartesian coordinates (x, y)?

Back

To convert from Polar to Cartesian coordinates, use the formulas: x = r * cos(θ) and y = r * sin(θ).

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.

Front

What does the radius r represent in Polar coordinates?

Back

The radius r represents the distance from the origin to the point in the Polar coordinate system.

Front

How do you find the distance between two points in Polar coordinates?

Back

To find the distance between two points (r1, θ1) and (r2, θ2), use the formula: d = √(r1² + r2² - 2*r1*r2*cos(θ2 - θ1)).

Front

What is the Polar equation of a circle centered at the origin?

Back

The Polar equation of a circle centered at the origin with radius a is given by: r = a.

Front

How do you graph Polar equations?

Back

To graph Polar equations, plot points for various values of θ, calculate the corresponding r, and then plot these points in the Polar coordinate system.

Front

What is the Polar equation of a line through the origin?

Back

The Polar equation of a line through the origin making an angle θ with the positive x-axis is given by: θ = constant.

Front

What is the Polar equation of a spiral?

Back

The Polar equation of a spiral can be expressed as r = aθ, where a is a constant.