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Published byJulian Toft Modified about 1 year ago

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Polar Coordinates In this section, we will study the following topics: Converting between polar and rectangular coordinates

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2 The Polar Coordinate System The polar axis corresponds to the positive x-axis. The pole corresponds to the origin.

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3 Polar Coordinates A point P in the polar coordinate system is represented by an ordered pair. If, then r is the distance of the point from the pole. is an angle (in degrees or radians) formed by the polar axis and a ray from the pole through the point.

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4 Example Plot the point P with polar coordinates

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5 Example (r, ) Polar axis Pole Plot the point with polar coordinates 4

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6 Polar Coordinates If, then the point is located units on the ray that extends in the opposite direction of the terminal side of .

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7 Example Plot the point P with polar coordinates P

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10 A)B) C) D)

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11 To find the rectangular coordinates for the point, we can use trig functions. Converting from Polar to Rectangular Coordinates

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15 Likewise, we can find the polar coordinates if we are given the rectangular coordinates using the trig functions. Example: Find the polar coordinates for the point for which the rectangular coordinates are given: (5, 4) Converting from Rectangular to Polar Coordinates (5, 4) x y

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16 Converting from Rectangular Coordinates to Polar Coordinates

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19 The TI-84 calculator has handy conversion features built-in. Check out the ANGLE menu. 5: Returns value of r given rectangular coordinates (x, y) 6: Returns value of given rectangular coordinates (x, y) 7: Returns value of x given polar coordinates (r, ) 8: Returns value of y given polar coordinates (r, ) Check the MODE for the appropriate setting for angle measure (degrees vs. radians).

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20 End of Section 10.1

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