sin(110) without a calculator:

Question

anonymous · Answer

i know that we can use sum or difference formulas but i just can't find the right numbers

barrycarter · Answer

This effectively requires finding sin(20), which is the root of a cubic equation. There are ways to write this as a non-decimal, but they are all complex (both literally and figuratively): http://fwd4.me/17p9

experimentx · Answer

definitely not an easy job http://math.stackexchange.com/questions/176889/for-which-angles-we-know-the-sin-value-algebraically-exact

anonymous · Answer

okay, then i'll just use calc for now :) thx

experimentx · Answer

yep ... you can use it. :) this involves finding the value of sin(5) using sin(15) ... http://www.wolframalpha.com/input/?i=x+%282+%281-2x%5E2%29%2B1%29+%3D+sqrt%286%29%2F4+-+sqrt%282%29%2F4

anonymous · Answer

but i need sin(110)

experimentx · Answer

yep ... 
sin(110) = cos(20) = sqrt( 1 - sin^2(20)) = sqrt(1 - sin^2(15 + 5))
I don't think this is easy.

anonymous · Answer

yep, i used the calculator :)

experimentx · Answer

i would too ..