Question

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].

Answer 1

Write a polar coordinate in simplest form:

`(3,(-\pi)/(3))\text{ }`

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

since π in radian is 180 degree in angle notation

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

Hence the two additional polar representations of the point are

`\begin{gathered} (3,(7\pi)/(3)) \\ (-3,\pi) \end{gathered}`