What are the components of the vector between the origin and the polar coordinate #(8, (5pi)/6)#?

1 Answer
Jul 24, 2016

#((-4sqrt3),(4))#

Explanation:

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

That is #(r,theta)to(x,y)#

#color(orange)"Reminder"#

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

Here r = 8 and #theta=(5pi)/6#
#color(blue)"----------------------------------------"#
#rArrx=8cos((5pi)/6)#

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(cos((5pi)/6)=-cos(pi-(5pi)/6)=-cos(pi/6))color(white)(a/a)|)))#

#rArrx=-8cos(pi/6)=-8xxsqrt3/2=-4sqrt3#
#color(blue)"------------------------------------------------------------------"#

and y = #8sin((5pi)/6)#

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(sin((5pi)/6)=sin(pi-(5pi)/6)=sin(pi/6))color(white)(a/a)|)))#

#rArry=8sin(pi/6)=8xx1/2=4#
#color(blue)"----------------------------------------------"#

Thus the components of the vector are #((-4sqrt3),(4))#