FLASHCARD for MAJOR GRADE - Polar Coordinates and Equations

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).

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

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

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

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

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

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

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.

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

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