Question

Find the rectangular coordinates of (9,150degress)

Answer 1

Given the Polar Coordinates:

`\mleft(9,150\degree\mright)`

You need to use the following formulas:

`\begin{gathered} x=r\cdot cos\theta \\ \\ y=r\cdot\sin \theta \end{gathered}`

Remember that Polar Coordinates have this form:

`(r,\theta)`

And Rectangular Coordinates have this form:

`(x,y)`

In this case, you can identify that:

`\begin{gathered} r=9 \\ \theta=150\text{\degree} \end{gathered}`

Therefore, you can substitute values into the formulas:

`\begin{gathered} x=9\cdot cos(150\text{\degree)} \\ \\ y=9\cdot sin(150\text{\degree)} \end{gathered}`

Evaluating, you get:

`\begin{gathered} x=-\frac{9\sqrt[]{3}}{2} \\ \\ y=(9)/(2) \end{gathered}`

Hence, the answer is:

`(-\frac{9\sqrt[]{3}}{2},(9)/(2))`