Problem getting a Trig question check in My Calc

For example if I am given:

$\displaystyle \text{G:}Cos(x)=\frac{-1}{6}$ and $\displaystyle x$ is in $\displaystyle \text{Quadrant III}$

$\displaystyle \text{U:}Sin\frac{x}{2}=?$ in quadrant III

I worked it out in by using the half angle formula and got $\displaystyle \frac{-\sqrt 21}{6}$

I usually use the old inverse trick on the calculator and check to see if the decimal I get matches the answer I got. But on several half angle problems I am getting an undefined message on my calc. What is the deal and how can I go about checking these...

Like what PerfectHacker did on this post http://www.mathhelpforum.com/math-he...i-89-calc.html

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Also one other question.... When I am using the double angle and half angle formulas, when I get what the single trig value is equal to such as $\displaystyle Cos(x)=\frac{-1}{6}$ and I am going to stick the value in a problem do I want to insert the negative or positive sign along with it depending on which quadrant I am talking about? For example in the problem above we are in the 3rd quadrant so both $\displaystyle Sin$ & $\displaystyle Cos$ both are negative. Would I want to insert them into the formulas as negative? But suppose we are in quadrant 1 where both $\displaystyle Sin$ & $\displaystyle Cos$ are positive. Would I want to put both values into the double or half-angle formulas as a postive?

I could use some real help with both questions if you could...

Thanks as always for the help!