## tan[1/2 arcsin(-7/25)]

1. The problem statement, all variables and given/known data

$$\tan[\frac{1}{2} \arcsin(\frac{-7}{25})]$$

3. The attempt at a solution

I'm not sure how to take 1/2 the arcsin, should this use the half-angle formula?

Normally I would draw a triangle using the sin value (-7/25), then find the tan value (24/25), but the 1/2 is throwing me off.

How do I start this? Is this 1/2 the sin value (-7/25)= -7/50, then solve for the tan(-7/50)?
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 Recognitions: Homework Help Science Advisor Use the tangent half angle formula. tan(x/2)=??
 Thanks, so i get $$-\sqrt{26}$$ Does that sound right?

Recognitions:
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## tan[1/2 arcsin(-7/25)]

 Quote by jrjack Thanks, so i get $$-\sqrt{26}$$ Does that sound right?
arcsin(-7/25) is about -0.3. If you take half of that and take the tangent, it's nowhere near -sqrt(26) which is about -5. Is it? You can check these solutions using rough estimates or a calculator.
 $$-\sqrt{\frac{1+\cos x}{1-\cos x}}$$ $$-\sqrt{\frac{1+\frac{24}{25}}{1-\frac{24}{25}}}$$ $$=-\sqrt{26}$$

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 Quote by jrjack $$-\sqrt{\frac{1+\cos x}{1-\cos x}}$$ $$-\sqrt{\frac{1+\frac{24}{25}}{1-\frac{24}{25}}}$$ $$=-\sqrt{26}$$
tan(0/2)=0. If you put x=0 into your supposed half angle formula, what do you get? Does it work?
 Sorry, I now realize I have my signs flipped in my formula. I think my answer should be:$$-\sqrt{\frac{1}{26}}$$

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 Quote by jrjack Sorry, I now realize I have my signs flipped in my formula. I think my answer should be:$$-\sqrt{\frac{1}{26}}$$
That doesn't work either because (1-24/25)/(1+24/25) isn't equal to 1/26. Now what's it really equal to??
 Sorry, I got in a hurry, between typing the tex and working the problem several different ways (wrong of course). It should equal 1/49, which means my answer should be $-\sqrt{\frac{1}{49}}$

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 Quote by jrjack Sorry, I got in a hurry, between typing the tex and working the problem several different ways (wrong of course). It should equal 1/49, which means my answer should be $-\sqrt{\frac{1}{49}}$