Chapter 1 Topics in Analytic Geometry

••MA112 Section 750001: Prepared by Dr.Archara Pacheenburawana 20• rotating the polar axis 5π/4 and then moving forward from the pole 3 units along theterminal side of the angle, or• rotating the polar axis π/4 and then moving backward from the pole 3 units along theextension of the terminal side.Terminal sideP(3,5π/4)5π/4Polar axisP(3,π/4)π/4Terminal sidePolar axisThis suggest that the point (3,5π/4) might also be denoted by (−3,π/4), with minussign serving to indicate that the point is on the extension of the angle’s terminal side ratherthan on the terminal side itself.In general, the terminal side of the angle θ +π is the extension of the terminal side ofθ, we define negative radial coordinates by agreeing thatto be polar coordinates for the same point.(−r,θ) and (r,θ+π)Relationship Between Polar and Rectangular CoordinatesFrequently, it will be useful to superimpose a rectangular xy-coordinate system on top ofa polar coordinate system, making the positive x-axis coincide with the polar axis. Thenevery point P will have both rectangular coordinates (x,y) and polar coordinates (r,θ).yP(r,θ) = P(x,y)ryθxxFrom the above Figure, these coordinates are related by the equationsx = rcosθ, y = rsinθ (2.4)