How do you convert $(7, 5/6 π)$ into cartesian form?

Question

1711 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-14T11:32:19

$:. (x,y) = (-7sqrt3/2,7/2).$

Let $(r,theta)$ be the given polar co-ords. & let $(x,y)$ be their Cartesian conversion.

Then, we know that $x=rcostheta, y=rsintheta.$

Hence, with $r=7, theta=5pi/6,$ we get, $x=7cos5pi/6, y=7sin5pi/6.$

$:. x=7cos(pi-pi/6), y=7sin(pi-pi/6).$

$:. x=7(-cos(pi/6)), y=7sin(pi/6).$

$:. x=-7sqrt3/2, y=7/2$
$:. (x,y) = (-7sqrt3/2,7/2).$

How do you convert (7, 5/6 π) (7, 5/6 π) into cartesian form?