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

Question

asked Sep 20, 2023 27.1k views

1 Answer

Timo Schilling · Answer 1 · 2023-09-27T10:48:09+0000

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

$(-(3√(3))/(2),\text{ -}(3)/(2))$