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

1 Answer
Topscooter
Dec 17, 2015

(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)).

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