My answer does not match the calculator on finding the answer of sin(x/2) when tanx=1/2.

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My answer does not match the calculator on finding the answer of sin(x/2) when tanx=1/2.

Mathematics
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Here's an idea. Post the complete original question. Then post what you believe is the correct answer.
I'll try to be as consice as possible: The formula for the half angle of sin is: \[\sqrt{\dfrac{1-\cos x}{2}}\]
I understand the normal procedure of finding the answer but it doesn't make that much sense, in fact, the answer I get from the formula is the answer the calculator gives me for cos(x/2).

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Other answers:

If tanx=1/2 and pi
Now, by substituting, I would get something like sqrt((1-(-2sqrt5/5))/2) or sqrt((5+2sqrt5)/10)
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