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apple_pi

  • 2 years ago

Simplify sin^2(54)+cos^2(72)

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  1. apple_pi
    • 2 years ago
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    Please don't just go sin 54 = blah and cos(72) = blah, so blah + blah = blahblah

  2. apple_pi
    • 2 years ago
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    @Callisto

  3. tukajo
    • 2 years ago
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    is 54 the actual number or is that in 54 degrees?

  4. apple_pi
    • 2 years ago
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    54 degrees

  5. zzr0ck3r
    • 2 years ago
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    So you just want to know how to computte this by hand?

  6. apple_pi
    • 2 years ago
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    yes

  7. apple_pi
    • 2 years ago
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    why did you go into radians?

  8. apple_pi
    • 2 years ago
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    so what is x equal to?

  9. tukajo
    • 2 years ago
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    I fluttered that up ignore me.

  10. tukajo
    • 2 years ago
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    Hopefully zrocker can help you X_X

  11. Callisto
    • 2 years ago
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    \[sin^2(54)+cos^2(72)\]\[=(cos(90-54))^2+cos^2(72)\]\[=cos^2(36)+cos^2(72)\] That looks nicer

  12. apple_pi
    • 2 years ago
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    Oh, wait... let me try now

  13. Callisto
    • 2 years ago
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    Okay :|

  14. apple_pi
    • 2 years ago
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    cos^2(36) + (2cos^2(36)-1)^2

  15. apple_pi
    • 2 years ago
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    am i right?

  16. Callisto
    • 2 years ago
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    Yes.

  17. apple_pi
    • 2 years ago
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    now... do we evaluate cos(36) or simplify more?

  18. Callisto
    • 2 years ago
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    Evaluate.

  19. apple_pi
    • 2 years ago
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    ok. is this straightforward or something we fancily work out?

  20. Callisto
    • 2 years ago
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    very fancy :|

  21. Callisto
    • 2 years ago
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    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.

  22. zzr0ck3r
    • 2 years ago
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    wow

  23. Callisto
    • 2 years ago
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    @apple_pi Come back :'(

  24. zzr0ck3r
    • 2 years ago
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    So in what class do we learn to play with this trick?

  25. Callisto
    • 2 years ago
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    I'm sorry, I don't know. I'm not from the US. But for me, I learnt it two years before university.

  26. apple_pi
    • 2 years ago
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    Sorry... I had to go for a while

  27. apple_pi
    • 2 years ago
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    Yeah that solved it! Thanks @Callisto

  28. Callisto
    • 2 years ago
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    You're welcome. FYI, this post is worth looking! http://openstudy.com/study#/updates/4fe6e718e4b02c91101b52cd

  29. apple_pi
    • 2 years ago
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    Got another one: http://openstudy.com/study#/updates/50827553e4b0dab2a5ebddaa

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