Lösung 4.3:4e
Aus Online Mathematik Brückenkurs 1
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Version vom 15:05, 22. Okt. 2008
The addition formula for sine gives us that
| \displaystyle \sin\Bigl(v+\frac{\pi}{4}\Bigr) = \sin v\cdot\cos\frac{\pi }{4} + \cos v\cdot\sin\frac{\pi}{4}\,\textrm{.} |
Because we know from exercise b that \displaystyle \sin v = \sqrt{1-b^2} we use that \displaystyle \cos (\pi/4) = \sin (\pi/4) = 1/\!\sqrt{2} to obtain
| \displaystyle \sin\Bigl(v+\frac{\pi }{4}\Bigr) = \sqrt{1-b^2}\cdot\frac{1}{\sqrt{2}} + b\cdot\frac{1}{\sqrt{2}}\,\textrm{.} |
