What are the components of the vector between the origin and the polar coordinate #(4, (-pi)/3)#?

1 Answer
Jim G.
Aug 19, 2016

#((2),(-2sqrt3))#

Explanation:

To convert from #color(blue)"polar to cartesian"#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))#

here r = 4 and #theta=-pi/3#

#rArrx=4cos(-pi/3)" and " y=4sin(-pi/3)#

#color(orange)"Reminder "#

#color(red)(|bar(ul(color(white)(a/a)color(black)(cos(-pi/3)=cos(pi/3)" and " sin(-pi/3)=-sin(pi/3))color(white)(a/a)|)))#

#rArrx=4cos(pi/3)=4xx1/2=2#

and #y=-4sin(pi/3)=-4xxsqrt3/2=-2sqrt3#

Thus the components of the vector are #((2),(-2sqrt3))#

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