What are the components of the vector between the origin and the polar coordinate #(7, (3pi)/4)#?
1 Answer
Aug 26, 2016
Explanation:
To convert from
#color(blue)"polar to cartesian coordinates"#
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))# here r = 7 and
#theta=(3pi)/4#
#rArrx=7cos((3pi)/4)" and " y=7sin((3pi)/4)#
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(cos((3pi)/4)=-cos(pi/4)" and " sin((3pi)/4)=sin(pi/4))color(white)(a/a)|)))#
#x=7cos((3pi)/4)=-7cos(pi/4)=-7xx1/sqrt2=(-7sqrt2)/2# and
#y=7sin((3pi)/4)=7sin(pi/4)=7xx1/sqrt2=(7sqrt2)/2# Thus the components of the vector are
#(((-7sqrt2)/2),((7sqrt2)/2))#
