Question

511Suppose a point has polar coordinates -3,with the angle measured in radians.3Find two additional polar representations of the point.Write each coordinate in simplest form with the angle in [-27, 2ne].ODUTOOХ(0

Answer 1

First we write the point

we use the yellow angle to find another measures

Now we write another points to represent it

the measure of the angle is pi(for the strigth line) less yellow angle

`\begin{gathered} x=\pi-(\pi)/(3) \\ \\ x=(2)/(3)\pi \end{gathered}`

then a new point is

`(3,(2)/(3)\pi)`

and we can find many values to the radians becaus if we add a turn(2pi) to the original angle we obtain a similar or equivalent angle then a secon point is

`\begin{gathered} (3,(2)/(3)\pi+2\pi) \\ \\ \\ (3,(8)/(3)\pi) \end{gathered}`