What are the components of the vector between the origin and the polar coordinate #(2, (-5pi)/6)#?
1 Answer
Sep 5, 2016
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 = 2 and
#theta=-(5pi)/6#
#rArrx=2cos(-(5pi)/6)" and " y=2sin(-(5pi)/6)#
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(cos(-(5pi)/6)=-cos(pi/6))color(white)(a/a)|)))# and
#color(red)(|bar(ul(color(white)(a/a)color(black)(sin(-(5pi)/6)=-sin(pi/6))color(white)(a/a)|)))#
#rArrx=-2cos(pi/6)=-2xxsqrt3/2=-sqrt3# and
#y=-2sin(pi/6)=-2xx1/2=-1# Thus the components of the vector are
#((-sqrt3),(-1))#
