Question

What are the components of the vector between the origin and the polar coordinate `(5, (5pi)/3)`?

Answer 1

`((5/2),(-(5sqrt3)/2))`

Explanation:

To convert Polar to Cartesian coordinates , use the formulae that link them.

`• x = rcostheta`

`• y = rsintheta`

here r = 5 and `theta = (5pi)/3`

`rArr x = 5cos((5pi)/3)" and " y = 5sin((5pi)/3)`
`"-----------------------------------------------------------------------"`

now `cos((5pi)/3) = cos(pi/3) " and " sin((5pi)/3) = -sin(pi/3)`

using `color(blue)" exact values for these ratios "`

`rArr cos(pi/3) = 1/2" and " -sin(pi/3) = -sqrt3/2`
`"-----------------------------------------------------------------------"`

`rArr x = 5cos((5pi)/3) = 5cos(pi/3) = 5xx1/2 = 5/2`

and `y = 5sin((5pi)/3) = -5sin(pi/3) = -5xxsqrt3/2 = (-5sqrt3)/2`