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Very basic trig question.. help needed! +rep

Discussion in 'General Discussions' started by creeping_death, Apr 12, 2010.

  1. creeping_death

    creeping_death Level I

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    Ok.. so I have a very basic trig question i am trying to figure out. I missed 2 days of class last week and am completely lost :( here is the question:

    sin40 + sin130 + sin220 + sin310

    use definition

    I know the answer is 0.. just need to know why and how to calculate w/o a calculator x__x I really wish i woulda gone to class now:(
     
  2. Hellz

    Hellz Newbie

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    Lol SinCos and Tangent are all basically codenames for A B and C (respectively i think, or it depends on the problem). I think tangent is always the hypotonuse, while the problem will normally tell you if your using Sin or Cos to solve the problem. Using a graphing clacultor is very useful for figuring out these problems. I don't know the answer to your question but I know google has some really good calculators.
     
  3. SoC

    SoC Moderator
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    Sketch the graph and all is obvious.

    Let sin40 = A
    Draw a dashed line at 90 degrees. (the middle of the first bump) And you'll see the graph is symmetricla either side of that.
    Therefore sin130 gives the same answer as sin(130-90)=sin40

    Now sin220 if you observe again it's symmetrical but upside down, you get that sin220=-sin(40),
    again sin310 is the same as sin220 which is the same as -sin40.

    so you have

    sin40+sin40-sin40-sin40=0

    :)
     
    creeping_death likes this.
  4. Mercury

    Mercury Level I

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    Ahh Soc beat me to it.
    These basic trig questions usually simplify and cancel out to something extremely simple :)
     
  5. creeping_death

    creeping_death Level I

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    Hehe.. thx i ended up looking this up a few hours before the hw was due and forgot to check this. but i'll rep you anyways ^^
     
  6. Wings

    Wings Level III

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    Actually it is sin40+sin50-sin40-sin50=0

    But it's basically the same :p
     
  7. SoC

    SoC Moderator
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    Good spot :D same difference though :p
     

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