Question

What are the components of the vector between the origin and the polar coordinate `(7, (3pi)/4)`?

Answer 1

`(((-7sqrt2)/2),((7sqrt2)/2))`

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))`