Question

What are the components of the vector between the origin and the polar coordinate `(8, (4pi)/3)`?

Answer 1

`((-4),(-4sqrt3))`

Explanation:

Using the formulae that link Polar to Cartesian coordinates.

`•x=rcostheta" and " y=rsintheta`

here r = 8 and `theta=(4pi)/3`

`rArrx=8cos((4pi)/3)" and " y=8sin((4pi)/3)`

now : `cos((4pi)/3)=-cos(pi/3)=-1/2`

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

`rArrx=8xx-1/2=-4`

and `y=8xx-sqrt3/2=-4sqrt3`

components of vector `=((-4),(-4sqrt3))`