Question

What are the components of the vector between the origin and the polar coordinate `(-2, (23pi)/12)`?

Answer 1

`(2cos((23pi)/12),2sin((23pi)/12))`

Explanation:

You can use complex numbers to simplify the problem. And by the way, a module is a non-negative number so `-2` is probably `2`.

Here, you're looking for the component of the complex number `2e^(i(23pi)/12)`. Its module is `2` and in general, `e^(itheta) = cos(theta) + isin(theta)`, so we can say that `2e^(i(23pi)/12) = 2(cos((23pi)/12) + isin((23pi)/12))`.

Unfortunately, `(23pi)/12` is not a usual value for `cos` and `sin` so I can only tell you that the components of this vector are `(2cos((23pi)/12),2sin((23pi)/12))`.