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math hw...need help

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dinhotheone:
i was doing my AP physics hw and i ran across a problem where you have to do projectile motion and figure out two angles whoch you can shoot water out of a hose and still get it in a bucket. it seemed not to hard until i simplified it to this:

sin(-54125+)cos(-54125+) = .21
(-54125+) = theta btw

to clarify: sin(theta)*cos(theta) = .21

now i know how to do this on the calc but i was wondering if anyone knew how i would go about getting the answer analytically.using inverses just seems like a bad idea and this is the one problem that has stumped me tonight/ this year so far. any math wiz's would be nice if they could help. usually i am good at math but i cant seem to figure this out. hmm i wonder if mathematica could help....anyway any help would be appreciated.

edit: no on that about mathematica

Ranman:
Would Soh Cah Toa help?

bfr:
*bfr tries to remember trig

"sin(theta)*cos(theta) = .21" Can be turned into:

sin(2*theta)/2=.21
sin(2*theta)=.42

If that helps.  

"using inverses just seems like a bad idea" From what I remember, inverses should probably work though.

Ranman:
Or what about this:

Product to Sum Identities:


Courtesy of Wikipedia:
http://en.wikipedia.org/wiki/Trigonometry

Edit: bfr beat me to it.  :P

dinhotheone:
thanks guys but you 2 were beaten to it by my little brother. on the way to school this morning i told him about it and he figured it out right away, apparently he just did  those precalc thoerems the day before or something. i totally forgot em.

@bfr, i meant inverses at the point where i was not once you have it simplified into a single trig function.

thanks for your help guys

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