Question

What are the components of the vector between the origin and the polar coordinate `(2, (-5pi)/6)`?

Answer 1

`((-sqrt3),(-1))`

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))`