Question

What are the components of the vector between the origin and the polar coordinate `(12, (3pi)/2)`?

Answer 1

`((0),(-12))`

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 = 12 and `theta=(3pi)/2`

`rArrx=12cos((3pi)/2)=0`

and `y=12sin((3pi)/2)=-12`

Thus the components of the vector `=((0),(-12))`