anonymous
  • anonymous
Simplify sin^2(54)+cos^2(72)
Trigonometry
schrodinger
  • schrodinger
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anonymous
  • anonymous
Please don't just go sin 54 = blah and cos(72) = blah, so blah + blah = blahblah
anonymous
  • anonymous
@Callisto
anonymous
  • anonymous
is 54 the actual number or is that in 54 degrees?

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anonymous
  • anonymous
54 degrees
zzr0ck3r
  • zzr0ck3r
So you just want to know how to computte this by hand?
anonymous
  • anonymous
yes
anonymous
  • anonymous
why did you go into radians?
anonymous
  • anonymous
so what is x equal to?
anonymous
  • anonymous
I fluttered that up ignore me.
anonymous
  • anonymous
Hopefully zrocker can help you X_X
Callisto
  • Callisto
\[sin^2(54)+cos^2(72)\]\[=(cos(90-54))^2+cos^2(72)\]\[=cos^2(36)+cos^2(72)\] That looks nicer
anonymous
  • anonymous
Oh, wait... let me try now
Callisto
  • Callisto
Okay :|
anonymous
  • anonymous
cos^2(36) + (2cos^2(36)-1)^2
anonymous
  • anonymous
am i right?
Callisto
  • Callisto
Yes.
anonymous
  • anonymous
now... do we evaluate cos(36) or simplify more?
Callisto
  • Callisto
Evaluate.
anonymous
  • anonymous
ok. is this straightforward or something we fancily work out?
Callisto
  • Callisto
very fancy :|
Callisto
  • Callisto
let x = 36 5x = 180 3x = 180 - 2x sin 3x = sin2x 3 sinx - 4sin^3 x = 2sinx cox Since sinx =/= 0 3- 4 sin^2 x = 2cosx 3- 4 ( 1-cos^2 x) = 2 cos x 4 cos^2 x - 2cosx -1 =0 Now, solve for cosx.
zzr0ck3r
  • zzr0ck3r
wow
Callisto
  • Callisto
@apple_pi Come back :'(
zzr0ck3r
  • zzr0ck3r
So in what class do we learn to play with this trick?
Callisto
  • Callisto
I'm sorry, I don't know. I'm not from the US. But for me, I learnt it two years before university.
anonymous
  • anonymous
Sorry... I had to go for a while
anonymous
  • anonymous
Yeah that solved it! Thanks @Callisto
Callisto
  • Callisto
You're welcome. FYI, this post is worth looking! http://openstudy.com/study#/updates/4fe6e718e4b02c91101b52cd
anonymous
  • anonymous

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