What is the Cartesian form of $( 12 , (23pi)/3 )$ ?

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Answer 1 · 2016-12-27T20:08:39

$(6,-10.4)$

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in polar forms, the first coordinate is always the hypotenuse.

$r=12$

$theta=(23pi)/3$

$x$ and $y$ can be solved as the adjacent and opposite, respectively.

using $sin$ and $cos$ ratios:

$sin (23pi)/3 = O /H = y/12$

$y = 12 * sin((23pi)/3)$

$= -10.4 (3s.f.)$

$cos (23pi)/3 = A/H = x/12$

$x = 12 * cos(23pi)/3$

$= 6$

cartesian coordinates: $(6, -10.4)$

What is the Cartesian form of ( 12 , (23pi)/3 ) ( 12 , (23pi)/3 ) ?