Lösung 4.3:3f

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In this case, it is perhaps simplest to use the addition formula for sine,
In this case, it is perhaps simplest to use the addition formula for sine,
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{{Displayed math||<math>\sin\Bigl(\frac{\pi}{3}+v\Bigr) = \sin\frac{\pi }{3}\cdot \cos v + \cos\frac{\pi}{3}\cdot\sin v\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>\sin\Bigl(\frac{\pi}{3}+v\Bigr) = \sin\frac{\pi }{3}\cdot \cos v + \cos\frac{\pi}{3}\cdot\sin v\,\textrm{.}</math>}}
Since <math>\sin (\pi/3) = \sqrt{3}/\!2</math>, <math>\cos (\pi/3) = 1/2</math>, <math>\sin v = a</math>, and <math>\cos v=\sqrt{1-a^2}</math> this can be written as
Since <math>\sin (\pi/3) = \sqrt{3}/\!2</math>, <math>\cos (\pi/3) = 1/2</math>, <math>\sin v = a</math>, and <math>\cos v=\sqrt{1-a^2}</math> this can be written as
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{{Displayed math||<math>\sin\Bigl(\frac{\pi}{3}+v\Bigr) = \frac{\sqrt{3}}{2}\sqrt{1-a^2} + \frac{1}{2}a\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>\sin\Bigl(\frac{\pi}{3}+v\Bigr) = \frac{\sqrt{3}}{2}\sqrt{1-a^2} + \frac{1}{2}a\,\textrm{.}</math>}}

Version vom 08:54, 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{.}
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.3:3f“