2
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I have

$\cos \frac{1234 \pi}{5} + i \cdot \sin \frac{1234 \pi}{5}$

I believe I can simplify the $1234$ further, but how?

  • 4
    $1234=246\cdot 5 + 4$2012-02-26

2 Answers 2

8

$\frac{1234\pi}5 = 246\pi + \frac{4\pi}5$

2

To complement mrf, we can say that $cos(\frac{1234 \pi}{5})=cos(\frac{4 \pi}{5}$). Because there are the periodic identities which stays that:

$\sin( \theta+ 2 \pi n)= \sin \theta $

$\cos( \theta+ 2 \pi n)= \cos \theta \qquad n \in \mathbb{Z}$

This happens because the period of sine and cosine funtions is $2 \pi$.

  • 0
    Steven Stadnicki you are right.I forgot to fit in the question.Its done2012-02-28