What is the Cartesian form of $( 6,-pi/3 )$ ?

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Answer 1 · 2018-07-18T14:45:54

$(3, -3\sqrt3)$

The Cartesian coordinates $(x, y)$ of the point $(6, -{\pi}/3)\equiv(r, \theta)$ are given as follows

$x=r\cos\theta$

$=6\cos(-{\pi}/3)$

$=6\cos(\pi/3)$

$=6\cdot 1/2$

$=3$

$y=r\sin\theta$

$=6\sin(-{\pi}/3)$

$=-6\sin(\pi/3)$

$=-6\cdot \sqrt3/2$

$=-3\sqrt3$

hence, the Cartesian coordinates are $(3, -3\sqrt3)$

What is the Cartesian form of ( 6,-pi/3 )( 6,-pi/3 )?