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Suppose a point has polar coordinates (6,5pi/6)with the angle measured in radians.Find two additional polar representations of the point.Write each coordinate in simplest form with the angle in (-2pi, 2pi).

Suppose A Point Has Polar Coordinates 65pi6with The Angle Measured In RadiansFind Two Additional Polar Representations Of The PointWrite Each Coordinate In Simp class=

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SOLUTION

To find the additional polar representation of a giving point we use the following

1. By adding or subtracting a multiple of 2π to θ

2. By using a negative radius r, and adding an odd multiple to π

Giving the polar coordinates

[tex](6,\frac{5\pi}{6})[/tex]

The additional coordination will be by adding 2π to θ

[tex]\begin{gathered} (6,\frac{5\pi}{6}+2\pi) \\ \\ (6,\frac{17\pi}{6}) \end{gathered}[/tex]

Hence one addition coordinate is (6,17π/6)

To find additional polar coordinates,

We subtract 2π from θ

[tex]\begin{gathered} (6,\frac{5\pi}{6}) \\ \text{Then} \\ (6,\frac{5\pi}{6}-2\pi) \\ \\ (6,\frac{5\pi-12\pi}{6})=(6,-\frac{7\pi}{6}) \end{gathered}[/tex]

Hence, another additional coordinate is (6,-7π/6 )

Therefore, the two additional polar coordinates are (6,17π/6) and (6,-7π/6 )

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