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# Starting my Trig watch

1. Heya! i'm just starting my new trig section
sorry if its not so clearly set out, as it's the second time i write this post. can't be bothered with latexing it all this time sorry
I''m stuck with this guys, so if could give me a nudge in the right dirrection i'd appreciate it.

Q:cos2x=cos(x+pi/3) find general soln
i did:

=>

hence

so

thus

giving general solutions of x=npi and x=npi/2+(-1)^n.0
which are not correct.
again i apologise for the quickness of writing this, as it was so nice and pretty before :'(
2. (Original post by Goldenratio)
Heya! i'm just starting my new trig section
sorry if its not so clearly set out, as it's the second time i write this post. can't be bothered with latexing it all this time sorry
I''m stuck with this guys, so if could give me a nudge in the right dirrection i'd appreciate it.

Q:cos2x=cos(x+pi/3) find general soln
i did:

=>

hence

so

thus

giving general solutions of x=npi and x=npi/2+(-1)^n.0
which are not correct.
again i apologise for the quickness of writing this, as it was so nice and pretty before :'(
some general solutions are;
x+ π/3 = 2nπ - 2x
=> 3x = 2nπ - π/3
=> x = 2nπ/3 - π/9

2nπ - (x+π/3) = 2x
2nπ - x - π/3 = 2x
2nπ - π/3 = 3x
=> x = 2nπ/3 - π/9 <= (same result as above)

2x = x + π/3 + 2nπ
=> x = π/3 + 2nπ

x+ π/3 = 2nπ + 2x
=> x = π/3 - 2nπ
3. (Original post by Goldenratio)
Q:cos2x=cos(x+pi/3) find general soln
(
If STEP taught me one thing, it was the whole "cosx = cosy doens't imply that x=y" argument. Then again, I undoubtedly failed STEP miserably this year so I'll give you a haphazard solution which doesn't feel right :

Considering the cos graph: The period of the graph y = cosx is 2π (i.e. How long it takes before the graph begins to 'loop'), so a general solution will have a multiple of 2pπ in it as a result. In other words, cosx = cosy => x = y + 2pπ

cos2x = cos(x + π/3)

=> 2x = (x + π/3) + 2pπ (p is included in the set of integers)

x = π[1/3 + 2p]

x = (π/3)[1 + 6p]

I reckon it's wrong though .
4. You can use the general result that if cosA=cosB, B=2npi-A,or B=2npi+A,nEZ.
5. Hey! Thank you guys very much for all your help! Wow that makes my sunday morning!

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Updated: July 10, 2005
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