Lösung 4.3:3f
Aus Online Mathematik Brückenkurs 1
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Version vom 15:04, 22. Okt. 2008
In this case, it is perhaps simplest to use the addition formula for sine,
| \displaystyle \sin\Bigl(\frac{\pi}{3}+v\Bigr) = \sin\frac{\pi }{3}\cdot \cos v + \cos\frac{\pi}{3}\cdot\sin v\,\textrm{.} |
Since \displaystyle \sin (\pi/3) = \sqrt{3}/\!2, \displaystyle \cos (\pi/3) = 1/2, \displaystyle \sin v = a, and \displaystyle \cos v=\sqrt{1-a^2} this can be written as
| \displaystyle \sin\Bigl(\frac{\pi}{3}+v\Bigr) = \frac{\sqrt{3}}{2}\sqrt{1-a^2} + \frac{1}{2}a\,\textrm{.} |
