Question

Solve the equation on the interval 0,2pi
2sin^2x=3(1-cosx)

Answer 1

you have this : 2(1- cos^2 x) = 3 -3cos x
its a quad eqn in cos x..
just solve for cos x,,and then for x..

Answer 2

altough you can directly find out cos x via hit and trial..ain't that difficult,,try it :D
(one of those traditional values)

Answer 3

you may use this:
1 - cos^2 x = (1+ cos x)(1- cos x)
note that you cant directly cancel (1-cos x) as it equals to 0 (which you'll find out later)

Answer 4

how did you get the (1+cosx)(1-cosx)?

Answer 5

a^2 - b^2 = (a+b)(a-b) <--- clearer now buddy?

Answer 6

ohhh i see I thought you turned the 3-3cosx into that but thats in place of the 1-cos^2x

Answer 7

i didnt get your query..?? come again..

Answer 8

i just wrote (1)^2 - (cos x)^2 as (1+cos x)(1- cos x)
that shouldnt be much of a problem..

Answer 9

Yeah I see what you mean now. How would I solve for x now?

Answer 10

what values of cos x did you get ?

Answer 11

none yet I'm stuck at that part

Answer 12

which part..write down where did you reach..??

Answer 13

I've only gotten to 2(1+cosx)(1-cosx)=3(1-cosx) you said I can't cancel right

Answer 14

yes you cant,,hmm
bring all terms on 1 side,,lets say LHS..now take (1-cos x) common,,what do you get?

Answer 15

??

Answer 16

2/3(1+cosx)(1-cosx)(1-cosx)?

Answer 17

not dividing,,i meant subtracting :D
subtract 3(1-cosx) from both sides,,and then take (1-cos x) common

Answer 18

<ding> ?
comeon buddy,,it isnt that tought..make an attempt..go for it..

Answer 19

:D

Answer 20

Would it just be 2(1-cos^2x)-3(1-cosx)?

Answer 21

yes ,,thats right,,now expand (1- cos^2 x) as (1-cos x)(1+cos x)..take out (1-cos x) common

Answer 22

ok so 2(1+cosx)-3=0?

Answer 23

actually since you cant cancel (1-cos x),,you'll have this :
(1- cos x)( 2 (1+cosx) -3) =0
so you get :
1-cosx =0 and 2(1+cos x) -3 =0
what values of cos x you get from here?

Answer 24

cos x = -1
cos x = 1/2?

Answer 25

cos x=1/2 is right,,
but -1 ?? it should be cos x=1..check again..

Answer 26

oh youre right I forgot to include the negative sign in front of cos which changes them both to positive

Answer 27

so then my final answers would be pi/3 and 5pi/3, since 2pi cant be included?

Answer 28

yep you are right,,since 0 and 2pi are not included,,these would be the ans.

Answer 29

awesome. Thanks a lot for being patient im so tired so it took me a while lol

Answer 30

nevermind,,glad to help ^_^