Archers, can you prove these trigonometric identities?

CornHilario - Heavens Tear
CornHilario - Heavens Tear Posts: 647 Arc User
edited August 2010 in Archer
Hey archers, I'm back with more maths... b:chuckle

1. tan^2(x/2) = 1-2cotx*cscx+2cot^2x

2.OK, here is a giant fraction.

1+sin2v+cos2v
= cotv
1+sin2v-cos2v

The string of -'s is the fraction bar. Didn't want to confuse anyone.


As always, if the question is unclear, just ask.
One corn to rule them all and in the darkness cream them

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Post edited by CornHilario - Heavens Tear on

Comments

  • CornHilario - Heavens Tear
    CornHilario - Heavens Tear Posts: 647 Arc User
    edited August 2010
    school starts in 1.333 hours, guys c'moooon.... b:sleep

    Calling all smart archers: Asterelle, Devoted, and Elenacostel. :P
    One corn to rule them all and in the darkness cream them

    [SIGPIC][/SIGPIC]
    MS paint ftw. Disclaimer: my suit is actually gray, not black.

    ♥: The best f♥♥king censor ever. Always remember to show
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  • Shandelzare - Sanctuary
    Shandelzare - Sanctuary Posts: 732 Arc User
    edited August 2010
    It's all trig identities.

    Go by the list in your book and simplify. I'm too lazy for this...
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  • CornHilario - Heavens Tear
    CornHilario - Heavens Tear Posts: 647 Arc User
    edited August 2010
    I had been, all morning. Didn't get it =\
    One corn to rule them all and in the darkness cream them

    [SIGPIC][/SIGPIC]
    MS paint ftw. Disclaimer: my suit is actually gray, not black.

    ♥: The best f♥♥king censor ever. Always remember to show
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  • Boogiepanda - Raging Tide
    Boogiepanda - Raging Tide Posts: 4,682 Arc User
    edited August 2010
    Lol you serious about this maths homework stuff?
  • CornHilario - Heavens Tear
    CornHilario - Heavens Tear Posts: 647 Arc User
    edited August 2010
    yes, i'm really serious lol.

    i CAN rely on archers to do my math.
    One corn to rule them all and in the darkness cream them

    [SIGPIC][/SIGPIC]
    MS paint ftw. Disclaimer: my suit is actually gray, not black.

    ♥: The best f♥♥king censor ever. Always remember to show
    love to eachother on the forum even when you are cussing eachother out.
  • Boogiepanda - Raging Tide
    Boogiepanda - Raging Tide Posts: 4,682 Arc User
    edited August 2010
    If you don't get maths, maybe you should reroll as an archer then maybe the maths god will bless you ;)
  • Drippydrop - Harshlands
    Drippydrop - Harshlands Posts: 23 Arc User
    edited August 2010
    I'm already confused

    and im only the tan^2(x/2) = 1-2cotx*cscx+2cot^2x.
    Need dem school calculators..
    Still wuldn't get it
  • XylolyX - Heavens Tear
    XylolyX - Heavens Tear Posts: 1,097 Arc User
    edited August 2010
    Boogiepanda - Raging Tide wrote: »
    If you don't get maths, maybe you should reroll as an archer then maybe the maths god will bless you ;)


    Nope I've got an 85 archer as an alt and I still have NO IDEA what all this means.b:victory
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  • Twil - Lost City
    Twil - Lost City Posts: 109 Arc User
    edited August 2010
    I'm an archer and I have no clue wtf you're talking about b:cry
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  • Zoe - Heavens Tear
    Zoe - Heavens Tear Posts: 3,814 Arc User
    edited August 2010
    Trig huh, I know this stuff I'd just have to get my notes. But I'm not doing this. :p
    Main characters
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  • fulgida
    fulgida Posts: 0 Arc User
    edited August 2010
    Those equations check out numerically, but they are double angle stuff and I never really got much joy out of double angle stuff.

    Where is my motivation here?
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited August 2010
    EDIT: Forum is eating my posts, I'll post a second time for the 2nd one

    1. tan^2(x/2) = 1-2cotx*cscx+2cot^2x

    Left-hand side
    tan(x/2)*tan(x/2)
    (cscx - cotx)*(cscx - cotx) <--- half angle of tan
    csc^2x - 2cscx*cotx + cot^2x <-- expand
    1 + cot^2x -2cscx*cotx + cot^2x = 1-2cotx*cscx+2cot^2x <-- the simpl. is obvious
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited August 2010
    EDIT: Forum keeps eating my post for the second one... QQ b:cry

    2.

    1+sin2v+cos2v
    = cotv
    1+sin2v-cos2v

    Lef-hand side

    1 + sinv*cosv + cos^2v - sin^2v <--- double angles of sin and cos
    1 + sinv*cosv - cos^2v + sin^2v
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Teppeii - Dreamweaver
    Teppeii - Dreamweaver Posts: 1,206 Arc User
    edited August 2010
    Decus - Dreamweaver wrote: »
    EDIT: Forum is eating my posts, I'll post a second time for the 2nd one

    1. tan^2(x/2) = 1-2cotx*cscx+2cot^2x

    Left-hand side
    tan(x/2)*tan(x/2)
    (cscx - cotx)*(cscx - cotx) <--- half angle of tan
    csc^2x - 2cscx*cotx + cot^2x <-- expand
    1 + cot^2x -2cscx*cotx + cot^2x = 1-2cotx*cscx+2cot^2x <-- the simpl. is obvious

    What is this I don't evenb:shocked
    On indefinite hiatus :3
  • LloydAsplund - Sanctuary
    LloydAsplund - Sanctuary Posts: 3,899 Arc User
    edited August 2010
    Teppeii - Dreamweaver wrote: »
    What is this I don't evenb:shocked

    You need be level 100 before.
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  • Esnemyl - Dreamweaver
    Esnemyl - Dreamweaver Posts: 3,079 Arc User
    edited August 2010
    Teppeii - Dreamweaver wrote: »
    What is this I don't evenb:shocked

    + whatever numbers I want to add .

    Deecusss stop flooding our poor minds with all this numbers @_@ ish so confusing.
    [SIGPIC][/SIGPIC]<3 by Silvy
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  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited August 2010
    Esnemyl - Dreamweaver wrote: »
    + whatever numbers I want to add .

    Deecusss stop flooding our poor minds with all this numbers @_@ ish so confusing.

    But math is so wonderful :3

    Can I be an honorary archer now? b:cute
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • greekgodkiller
    greekgodkiller Posts: 0 Arc User
    edited August 2010
    I couldn't even begin to f*cking understand that.....


    I know for sure i'm gonna skip trig now @_@.....
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited August 2010
    greekgodkiller wrote: »
    I couldn't even begin to f*cking understand that.....
    I know for sure i'm gonna skip trig now @_@.....

    It's actually 95 percent algebra. For example, the only actual trig in the first one is the half-angle tangent conversion. Other than that, it's the same as expanding a polynomial and grouping like terms.
    I still can't understand why I cannot type more than a few lines at work or home >.>
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Olba - Sanctuary
    Olba - Sanctuary Posts: 1,776 Arc User
    edited August 2010
    I should know how to do that. I really should. But then again, I never liked trigonometry and proving identities isn't exactly fun either.

    So I don't.

    b:cute
    If you disregard what I say because of who I am or because of the contents of what I said, you are a fool.

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  • truekossy
    truekossy Posts: 7,021 Arc User
    edited August 2010
    Decus - Dreamweaver wrote: »
    But math is so wonderful :3

    Can I be an honorary archer now? b:cute

    Yes. Yes you can.

    On a relevant side note, nice sig. b:cute
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited August 2010
    truekossy wrote: »
    Yes. Yes you can.

    On a relevant side note, nice sig. b:cute

    Was an epic quote, thank you you sir. b:cool
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • CornHilario - Heavens Tear
    CornHilario - Heavens Tear Posts: 647 Arc User
    edited August 2010
    oh....i just checked back on my thread. summer school ended last week. but ty lol

    im adding u onto my smart pwi guys list, BTW
    One corn to rule them all and in the darkness cream them

    [SIGPIC][/SIGPIC]
    MS paint ftw. Disclaimer: my suit is actually gray, not black.

    ♥: The best f♥♥king censor ever. Always remember to show
    love to eachother on the forum even when you are cussing eachother out.
  • Haliaeetus - Sanctuary
    Haliaeetus - Sanctuary Posts: 4 Arc User
    edited August 2010
    I don't want to be a math ****, but I thought I flex my math muscles a little since it seems an unusual topic in this forum. Be careful with that sig pic. It only holds in the special case when f is holomorphic in the region bounded by \gamma. More generally:

    2u4lvr8.jpg
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited August 2010
    Haliaeetus - Sanctuary wrote: »
    I don't want to be a math ****

    Oh I know, I just rather like this =3

    I am by no means an expert in complex analysis
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray

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