Question

What are the components of the vector between the origin and the polar coordinate `(6, (3pi)/4)`?

Answer 1

`((-3sqrt2),(3sqrt2))`

Explanation:

using the formulae that links Polar to Cartesian coordinates.

`• x = rcostheta`

`• y = rsintheta`

in this question: r = 6 and `theta = (3pi)/4`

`rArr x = 6cos((3pi)/4) = 6.(- 1/sqrt2) = -3sqrt2`

[note : `1/sqrt2 = sqrt2/(sqrt2 .sqrt2) = 1/2 sqrt2]`

and using exact values for `cos((3pi)/4)color(black)(" and ") sin((3pi)/4)`

`rArr y = 6sin((3pi)/4) = 6.(1/sqrt2) = 3sqrt2`