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Suppose a point has polar coordinates (3,-pi/3)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 3pi3with the angle measured in radiansFind two additional polar representations of the pointWrite each coordinate in simpl class=

Respuesta :

Write a polar coordinate in simplest form:

[tex](3,\frac{-\pi}{3})\text{ }[/tex]

The two additional polar representations of the point can be deduced as:

since π in radian is 180 degree in angle notation

[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex][tex]-\frac{\pi}{3}=-\frac{180}{3}=60^0[/tex][tex]\begin{gathered} (3,\frac{7\pi}{3}) \\ (-3,\pi) \end{gathered}[/tex]

Hence the two additional polar representations of the point are

[tex]\begin{gathered} (3,\frac{7\pi}{3}) \\ (-3,\pi) \end{gathered}[/tex]

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