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))
