What are the components of the vector between the origin and the polar coordinate #(6, (2pi)/3)#?
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 = 6 and
#theta=(2pi)/3#
#color(blue)"-------------------------------------"#
#rArrx=6cos((2pi)/3)#
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(cos((2pi)/3)=-cos(pi-(2pi)/3)=-cos(pi/3))color(white)(a/a)|)))#
#rArrx=-6cos(pi/3)=-6xx1/2=-3#
#color(blue)"--------------------------------------------------------------"# and y
#=6sin((2pi)/3)#
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(sin((2pi)/3)=sin(pi-(2pi)/3)=sin(pi/3))color(white)(a/a)|))#
#rArry=6sin(pi/3)=6xxsqrt3/2=3sqrt3#
#color(blue)"----------------------------------------------------"# Thus the components of the vector
#=((-3),(3sqrt3))#
