Solution 4.3:3f
From Förberedande kurs i matematik 1
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- | {{ | + | 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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+ | 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>}} |
Current revision
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{.} |