Question

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.(-3, 6)

Answer 1

Given

Polar coordinates

`(-3,(\Pi)/(6))`

Find

convert it into cartesian coordinates

Step-by-step explanation

As, it is in a polar form , so we use following formulas to convert it into cartesian coordinates

`\begin{gathered} x=rcos\theta \\ y=rsin\theta \end{gathered}`

as, we have given

`r=-3\text{ and }\theta=(\Pi)/(6)`

so,

`\begin{gathered} x=-3cos((\Pi)/(6))=-3*(√(3))/(2)=-(3√(3))/(2) \\ y=-3sin((\Pi)/(6))=\text{ -3}*(1)/(2)=-(3)/(2) \end{gathered}`

so, the cartesian coordinates are

`(-(3√(3))/(2),\text{ -}(3)/(2))`

Final Answer

Therefore the cartesian coordinates are

`(-(3√(3))/(2),\text{ -}(3)/(2))`