What is the Cartesian form of $( 9 , (16pi)/6 )$ ?

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Answer 1 · 2016-05-23T15:29:11

Cartesian form $(x, y)=(-9/2, (9sqrt3)/2)$

We start from the given $(9, (16pi)/6)$

$r=9$ and $theta=(16pi)/6=(8pi)/3$

solve for x

$x=r*cos theta$
$x=9*cos ((8pi)/3)=9*cos ((2pi)/3)=9*(-1/2)=-9/2$

solve for y

$y=r*sin theta$
$y=9*sin ((8pi)/3)=9*sin ((2pi)/3)=9*(sqrt3/2)=(9sqrt3)/2$

God bless....I hope the explanation is useful.

What is the Cartesian form of ( 9 , (16pi)/6 ) ( 9 , (16pi)/6 ) ?