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**In this section, we will study the following topics:**

MAT 204 F08 10.1 Polar Coordinates In this section, we will study the following topics: Converting between polar and rectangular coordinates

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**The Polar Coordinate System**

The pole corresponds to the origin. The polar axis corresponds to the positive x-axis.

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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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Example Plot the point P with polar coordinates

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

MAT 204 F08 Example Plot the point with polar coordinates 4 (r, ) Polar axis Pole

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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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Example Plot the point P with polar coordinates P

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MAT 204 F08

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A) B) D) C)

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**Converting from Polar to Rectangular Coordinates**

MAT 204 F08 Converting from Polar to Rectangular Coordinates To find the rectangular coordinates for the point, we can use trig functions.

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**Converting from Rectangular to Polar Coordinates**

MAT 204 F08 Converting from Rectangular to Polar Coordinates 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) (5, 4) x y

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**Converting from Rectangular Coordinates to Polar Coordinates**

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**5: Returns value of r given rectangular coordinates (x, y) **

MAT 204 F08 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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MAT 204 F08 End of Section 10.1

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