MA 16200 Lecture 33: lesson 33 notes
19 Apr 2016
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The coordinate system we are used to is called cartesian or rectangular. Look at the point (1,1) on the cartesian system: The angle between the x-axis and the line connecting (0,0) to this point is pi/4. The length of the line connecting (0,0) to this point is sqrt(2) So the polar coordinates of the point (1,1) are (sqrt(2), pi/4) Polar coordinates describe the location of a point in terms of a directed angle (theta) and a directed distance along the theta line (r) A point (p) has polar coordinates (r, theta) A negative r means you go in the reverse direction (across the origin, or pole ) In general (r, theta) and (r, theta + 2pi) are the same point; it is just completing another rotation to get there. Any point with r = 0 is on the pole , it doesnt matter the angle because it has no length. R^2 = x^2 + y^2 (distance formula)
