In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, 225°)

Key Concepts

Polar Coordinates

Polar coordinates represent a point in a two-dimensional space using a distance from a reference point (the origin) and an angle from a reference direction (usually the positive x-axis). The format is (r, θ), where 'r' is the radial distance and 'θ' is the angle in degrees or radians. Understanding how to interpret these coordinates is essential for locating points on a polar graph.

Conversion to Cartesian Coordinates

To analyze points in polar coordinates, it can be helpful to convert them to Cartesian coordinates (x, y). The conversion formulas are x = r * cos(θ) and y = r * sin(θ). This transformation allows for easier visualization and comparison with standard Cartesian graphs, which is often necessary for identifying points labeled A, B, C, or D.

Angle Measurement in Polar Coordinates

In polar coordinates, angles are measured from the positive x-axis, with counterclockwise being the positive direction. An angle of 225° indicates a point located in the third quadrant of the Cartesian plane, where both x and y coordinates are negative. Understanding the quadrant system and angle measurement is crucial for accurately determining the location of the point represented by the given polar coordinates.