1. Section 9.1 Polar Coordinates
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2. 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.
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3. Pole: origin in rectangular coordinates
Polar axis: positive x-axis in rectangular coordinates
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4. 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.
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8. clockwise is a negative angle measure, and
Remember that
clockwise is a negative angle measure,
and
counterclockwise is a positive angle measure.
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11. (A point has exactly one pair of rectangular coordinates but infinitely many pairs of polar coordinates.)
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23. 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.
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24. This is a circle.
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26. Homework: 9.1:(567):9-31(odds), 37, 39, 47, 57, 59, 61, 69, 75, 79
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