Question

What are the components of the vector between the origin and the polar coordinate `(9, (-3pi)/4)`?

Answer 1

`((-9/2sqrt2),(-9/2sqrt2))`

Explanation:

Using the formulae that link Polar to Cartesian coordinates.

`• x = rcostheta`

`• y = rsintheta`

here r = 9 and `theta = -(3pi)/4`

hence `x = 9cos(-(3pi)/4) " and " y = 9sin(-(3pi)/4)`
`"----------------------------------------------------------------------"`

now `cos(-(3pi)/4) = -cos(pi/4)`

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

The 'exact' value of `sin(pi/4) = cos(pi/4) = 1/sqrt2`
`"-------------------------------------------------------------------------"`

thus `x = -9cos(pi/4) = -9xx1/sqrt2 = -9/2 sqrt2`

and y `-9sin(pi/4) = -9xx1/sqrt2 = -9/2 sqrt2`