JMerrill, 2010 Coordinate Conversion To convert from polar to rectangular: x = r cosθ y = r sinθ To convert from rectangular to polar: y tanθ = x x2 + y2 = r2 2, 53 There are many ways to represent the point 2, 3 . 2 2, 3 2, 3 2, 53 (r, ) r, 2n When converting from one coordinate system to the other, we will only use 1 point instead of multiple representations. 1 2 3 0 3 2 3 There are 3 tests for symmetry, but they don’t always work, so we’ll use the Quick Test For equations like r = f(sin θ) • Graph is symmetric to the line y For 2 equations like r = g(cos θ) • Graph is symmetric to the polar (x) axis See Ex. 2 on page 786—a good use of sketching using symmetry. Example: Find the zeros and the maximum value of r for the graph of r = 2cos . 2 The maximum value of r is 2. It occurs when = 0 and r 0 when and 3 . 2 2 2. 1 These are the zeros 2 3 0 of r. 3 2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Symmetric about the polar axis 6