Polar Coordinates and Graphs
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Lesson Summary:
In this lesson on polar coordinates and graphs, learners are introduced to the difference between polar and rectangular coordinates. They learn how to convert between the two coordinate systems and how to plot points in polar coordinates on a polar grid. The lesson also covers polar equations and graphs, including circles, lines, and limacons, and explains how to rotate polar graphs and identify the center and radius of a circle.
Lesson Description:
Polar vs. rectangular coordinates; polar graphs; slope of the tangent line to a polar curve.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Questions answered by this video:
- What are polar coordinates?
- How do you change from rectangular to polar coordinates?
- How do you write (1,1) with polar coordinates?
- How do you graph the polar equation r = 1?
- How do you graph the polar equation theta = 30 degrees?
- How do you convert r = 2cos theta to rectangular coordinates and graph?
- How do you graph polar equations?
- What is a limacon?
- What is a cartioid?
- How do you graph r = 1 + cos theta?
- How do you graph r = 1 - sin theta?
- What does the graph of r = cos (2 theta) look like?
- How do you find a polar equation that satisfies given criteria?
- What is a lemniscate?
- How do you find horizontal and vertical tangents of polar graphs?
- How do you find the slope of a polar graph?
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Staff Review
The differences between rectangular and polar coordinates are explained as an introduction to polar. The big ideas are that x = rcos theta, y = rsin theta, r^2 = x^2 + y^2, and tan theta = y/x. Several examples are shown, with coordinates (r, theta). Then, some polar equations and graphs are shown and explained. Several equations and graphs are explained, as well as common polar graphs, limacons and cartioids. Roses are also shown for polar equations r = sin (k*theta). Horizontal and vertical tangents and slope of polar graphs are also discussed. This is a very full, important lesson. -
