Question

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

Answer 1

`((2),(-2sqrt3))`

Explanation:

To convert from `color(blue)"polar to cartesian"`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))`

here r = 4 and `theta=-pi/3`

`rArrx=4cos(-pi/3)" and " y=4sin(-pi/3)`

`color(orange)"Reminder "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos(-pi/3)=cos(pi/3)" and " sin(-pi/3)=-sin(pi/3))color(white)(a/a)|)))`

`rArrx=4cos(pi/3)=4xx1/2=2`

and `y=-4sin(pi/3)=-4xxsqrt3/2=-2sqrt3`

Thus the components of the vector are `((2),(-2sqrt3))`