How do you convert $(4, 4pi/3)$ into rectangular forms?

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Answer 1 · 2015-12-06T10:41:42

$x=-2$
$y=-2sqrt(3)$

If you know the poalr coordinates $(\rho,\theta)$ , then the transformation to have the rectangular ones is

$x=rcos(theta)$
$y=rsin(theta)$

In your case,

$x=4cos((4pi)/3)$
$y=4sin((4pi)/3)$

since $cos((4pi)/3)=-1/2$ , and $sin((4pi)/3)=-sqrt(3)/2$ , we have

$x=4*(-1/2)=-2$
$y=4*(-sqrt(3)/2)=-2sqrt(3)$

How do you convert (4, 4pi/3)(4, 4pi/3) into rectangular forms?