Pre-Calc Exam Notes 149

Pre-Calc Exam Notes 149 - Polar Coordinates Section 6.4 149...

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Unformatted text preview: Polar Coordinates Section 6.4 149 x y O y x r ( r , ) ( x , y ) Figure 6.4.6 Figure 6.4.6 shows how to convert between polar coordinates and Cartesian coordinates. For a point with polar coordinates ( r , ) and Cartesian coordinates ( x , y ): Polar to Cartesian: x = r cos y = r sin (6.9) Cartesian to Polar: r = radicalBig x 2 + y 2 tan = y x if x negationslash= (6.10) Note that in formula (6.10), if x = 0 then = /2 or = 3 /2. Also, if x negationslash= 0 and y negationslash= 0 then the two possible solutions for in the equation tan = y x are in opposite quadrants (for < 2 ). If the angle is in the same quadrant as the point ( x , y ), then r = radicalbig x 2 + y 2 (i.e. r is positive); otherwise r = radicalbig x 2 + y 2 (i.e. r is negative). Example 6.15 Convert the following points from polar coordinates to Cartesian coordinates: (a) (2,30 ); (b) (3,3 /4); (c) ( 1,5 /3) Solution: (a) Using formula (6.9) with r = 2 and...
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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