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I guess this is a really dumb question, but i've been trying quite a lot and I can't figure out how to determine the solutinons.

I need to determine the values of two angles and they don't seem to be ok. But I do know for sure that the values are right. The equation is as it follows:

$\begin{align*} &\sin(\alpha)=1/3\;;\\ &\cos(\alpha)\cos(\beta)=0\;;\text{ and}\\ &\cos(\alpha)\sin(\beta)=0.94280899908173\;. \end{align*}$

Because if $\sin(\alpha)$ is not $1$, neither will $\cos(\alpha)$ be $0$. Also means that $\cos(\beta)$ is $0$, resulting that $\sin(\beta)$ is $1$. Determined by calculus that $\cos(\alpha)$ is not $0.94280899908173$, I seem to be in a real trouble..

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    It is much more complicated, because I will recursively make larger molecule and i need all the coordinates and angles so I will be able to have the very same algorithm when dealing with other types of bounds (double or triple which have different angles). And there are also other details that are part of my program mechanism in favor of this type of approaching the problem2012-12-01

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Your reasoning to the effect that $\cos\beta=0$ is correct, and it follows that $\sin\beta=\pm1$. Since $\sin\alpha=\frac13$, you know that $\cos^2\alpha=1-\sin^2\alpha=\frac89$, and therefore $\cos\alpha=\pm\frac{2\sqrt2}3\approx\pm0.9428090415821$ and $\cos\alpha\sin\beta\approx0.9428090415821$ as well. Your figure of $0.94280899908173$ simply isn’t quite correct, though it’s close: the three values that you give aren’t quite consistent.

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    @Bujanca: You’re welcome.2012-12-01