cant find all solutions - pls help

hi - i cant see why in the equations:
cos x = 1/4 and sinx = 1/6 there are four answers for each.
I can get 2 on each of them but i dont see where for example in the first one - the answers 0 and 180 come from. The second one has answers pi/2 and 3pi/2 which i cant see where they come from. Can sum1 clarify where they have come form pls.

Reply 1

ryan750

ok - here is the whole question:

solve the equation 2sin2x = sinx (from 0 - 360)

the other is :

3sin2x = cosx (from 0 - 2pi)

Reply 2

m:)ckel

2sin2x = sinx
4sinxcosx = sinx (using double angle identity)

sinx(4cosx-1) = 0

sinx=0 or cosx = 1/4

x = 0, 75.5, 180, 284.5

I'm guessing you missed solutions by cancelling the sinx's. You have to factorise them out, as above. That's likely to be the cause of your missed solutions in the other question as well.