What is the Cartesian form of $( 2 , (13pi)/3 )$ ?

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Answer 1 · 2016-10-13T11:44:14

$"Polar:" (r,theta)=(2,(13pi)/3)color(white)("X")harr"Cartesian:" (x,y)=(1,sqrt(3))$

$theta= (13pi)/3 = 2xx(2pi)+pi/3$

Since $2pi$ represents a complete circle
$(13pi)/3$ is equivalent (in terms of location) to $pi/3$

Here is the standard $pi/3$ triangle (with $r=2$ )
enter image source here
from which we can see $x=1$ and $y=sqrt(3)$

What is the Cartesian form of ( 2 , (13pi)/3 ) ( 2 , (13pi)/3 ) ?