well this is one problem i have no idea how to start. i tried using the sum of angles but i cannot find anything that would help me get a start on the problem. im asked to find the exact value of cos 36? i thought about double angle identities..i cannot think of anything that would work for this problem. any help would be appreciated. thx in advance...
well if i was solving for theta, cos 5theta = -1 then i would say con inverse of (-1) = 5 theta, and then divide both sides by 5 to get theta, but i dont see the connection? im still missing the big picture....oh and yeah i tried the double angle, i used double angle to solve and figure out with cos 15 was...the 36 is really throwing me off, maybe if i add it something and then subtract it, i could try to use a difference formula...one of the guys in class said something about using the quadratic equation to solve the problem??? i really dont see the connection there...
ok wait now that i thought about it a little more, i would break it apart and make it the sum of angles..cos (4theta + theta) = -1 then i use the add properties and break it apart and so on...once i broke it apart i would have to use some substitution for the 4 theta..but i still dont see the connection...
Sorry, I must have been too vague. In fact this question is more difficult than I first suspected.
I was trying to get you to realise that 36 x 5 = 180.
Let degrees
So we have
We also (well I also) know that (you get this by angle sums like you've tried. I'll recommend cos (3x+2x), more efficient).
So letting x = cos = cos 36 we have
which factorises to
Can you continue?