Section 9.1 Polar Coordinates

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Section 9.1 Polar Coordinates Copyright © 2013 Pearson Education, Inc. All rights reserved

Plot points using polar coordinates. Objectives Plot points using polar coordinates. Convert from polar coordinates to rectangular coordinates. Convert from rectangular coordinates to polar coordinates. Transform equations between polar and rectangular forms. Copyright © 2013 Pearson Education, Inc. All rights reserved

Pole: origin in rectangular coordinates Polar axis: positive x-axis in rectangular coordinates Copyright © 2013 Pearson Education, Inc. All rights reserved

In the polar coordinate system, the polar coordinates are (r,θ). If r>0, r is the distance from the point to the pole. θ is the angle formed by the polar axis and a ray from the pole through the point. If r<0, the point is on the ray from the pole extending in the opposite direction. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

clockwise is a negative angle measure, and Remember that clockwise is a negative angle measure, and counterclockwise is a positive angle measure. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

(A point has exactly one pair of rectangular coordinates but infinitely many pairs of polar coordinates.) Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Transforming equations between polar and rectangular forms We know that and if Common techniques for transforming between polar and rectangular forms are multiply both sides of the equation by r, or square both sides of the equations. Copyright © 2013 Pearson Education, Inc. All rights reserved

This is a circle. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Homework: 9.1:(567):9-31(odds), 37, 39, 47, 57, 59, 61, 69, 75, 79 Copyright © 2013 Pearson Education, Inc. All rights reserved

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