Polar Coordinates and Graphs

Exercise on Polar Coordinates

Section 1: Plotting Polar Points

  • Point to Plot: (-4, 60°)
    • The point has a negative radius (r = -4).
    • To find an equivalent point with a positive r, add 180° to the angle:
    • New angle = 60° + 180° = 240°
    • Equivalent Point with Positive r: (4, 240°)

Section 2: Basic Polar Graphs

  • Matching Equations to Descriptions:
    1. Equation a): r = 7
    • Description: Circle, radius 7, centered at origin.
    1. Equation b): r = 3 sine (\theta)
    • Description: Circle, diameter 3, through origin, aligned on the y-axis.
    1. Equation c): r = 5 cose (\theta)
    • Description: Circle, diameter 7, through origin, aligned on the x-axis.

Section 3: Graphing Polar Equations

  • Graphing Equation: r = 4 cose (\theta)
    • Steps to Sketch the Graph:
    • Optionally create a table of values for different angles.
    • Fill in angles from 0° to 360° to find corresponding r values.
    • Plot the points on a polar coordinate grid.
    • Description of the Graph:
    • Circle center: at the origin
    • Diameter: 8 (since r = 4 from the origin to the edge, thus full diameter is 4 * 2)
    • Rests on the x-axis since it is defined by the cosine function.