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