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))
