i need help with pre-calculus

Discussion in 'ten-forward' started by WSFuser, Feb 19, 2006.

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  1. WSFuser

    WSFuser Registered Member

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    i have an equation:

    x = 1.54(1 - cos Θ) + 2sin² Θ

    I have to find an angle theta (Θ) between 0° and 360° that satifies the equation when x = 2. if anyone can help me that would be great.
     
  2. aka:snowman

    aka:snowman Former Poster

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    edit edit edit edit
     
    Last edited: Feb 19, 2006
  3. big ed

    big ed Registered Member

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    The answer is "Q"! Trust me!!
     
  4. WSFuser

    WSFuser Registered Member

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    i need someone to show me how to simply the expression, not how to use a calculator.
     
  5. aka:snowman

    aka:snowman Former Poster

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    edit edit edit edit
     
  6. ~*Nat*~

    ~*Nat*~ Registered Member

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  7. snowbound

    snowbound Retired Moderator

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  8. WSFuser

    WSFuser Registered Member

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  9. WSFuser

    WSFuser Registered Member

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    with help from another forum, i got this far:

    2 / 1.54 = sin² Θ + 2sin² Θ
     
  10. BlueZannetti

    BlueZannetti Administrator

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    Not quite..., I'd find another source.

    55.02349 degrees. Now show your work.....

    Blue
     
  11. WSFuser

    WSFuser Registered Member

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    2 = 1.54(1 - cos Θ) + 2sin² Θ

    if i divide 1.54 from both sides i get

    2 / 1.54 = (1 - cos Θ) + 2sin² Θ

    then remembering that sin² Θ + cos² Θ = 1, i can substitute in sin² Θ for 1 - cos Θ.

    2 / 1.54 = sin² Θ + 2sin² Θ

    thats all i got
     
  12. Marja

    Marja Honestly, I'm not a bot!!

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    LOL! Hey Fuser, don't ya hate when they want to see 'how you got your answer'?

    BlueZ must have said that or had it said to him, at some time......:)
    (He said that pretty fast!)

    Here is a help forum, if ya need more.......:D

    http://www.artofproblemsolving.com/Forum/forum-66.html

    Yes, DO show us your work when ya get 'it'! OK?;)


    Marja:cool:
     
  13. BlueZannetti

    BlueZannetti Administrator

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    You dropped a power.

    sin² Θ + cos² Θ = 1, rearranging, sin² Θ = 1 - cos² Θ, not 1 - cos Θ.

    You're on the right conceptual track though, so you're most of the way there. Get the equation in terms of one of the transcendental functions, but you really should look at substituting that sin² Θ term with (1 - cos² Θ), that yields a simple quadratic in cos Θ. Make the temporary variable transformation z = cos Θ and solve the quadratic for z. That solution has two branches, but only one is physically correct (i.e. shows the right bounding behaviour for cos Θ; that is, being in the bounded domain of -1 to 1).

    Blue
     
  14. WSFuser

    WSFuser Registered Member

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    d'oh, i missed that. thanx for the help tho
     
  15. Cochise

    Cochise A missed friend

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    I'd love to help but I know absolutely nothing about Egyptian Heiroglyphicals...


    Cochise,:cool: Tootin' Carmen in Carmel...
     
  16. SpikeyB

    SpikeyB Registered Member

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    Shouldn't dividing both sides by 1.54 yield: 2 / 1.54 = (1 - cos Θ) + 2sin² Θ/1.54 ?
     
  17. WSFuser

    WSFuser Registered Member

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    it doesnt matter cuz theta is a greek letter not egyptian
    the two 1.54 cancel out to give one as the denominator
     
  18. SpikeyB

    SpikeyB Registered Member

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    That would be the case if the rhs of the equation was:

    1.54((1 - cos Θ) + 2sin² Θ)
     
  19. probprince

    probprince Registered Member

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    hey WSFuser

    lol, yes, i remember the days of pre-calc. ok so i think here is how you do it:

    you have 1.54 - 1.54cosӨ -2sin^2Ө = 2
    ok, this reminds me of a quadratic equation, so we want to have a variable in place of cosӨ. However, we also have sinӨ in the equation. So, you can use one of the basic principles sin^2Ө +cos^2Ө = 1 and solve for sin^2Ө. you should get sin^2Ө = 1-cos^2Ө. but you have 2sin^2Ө in the equation, so your equivalent becomes 2-2cos^2Ө. plug this into the equation and everything becomes:

    2cos^2Ө - 2 - 1.54cosӨ + 1.54 = 2
    bring the two to the left side and substitute a temporary variable (such as a) for cosӨ and you will have a neat quadratic equation to use the quadratic formula:

    2a^2 - 1.54a - 2.46 = 0

    The rest is based on simple algebra and the quadratic equation. Check my work, i think the basic concept is correct though.
    Hope this helped. ;)



    edit: wow, i almost forgot, you have to substitute your variable back into the equation for a = cosӨ. you might have two answers (because of the quadratic equation) and check the validity of the solutions.
     
  20. ~*Nat*~

    ~*Nat*~ Registered Member

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  21. Firecat

    Firecat Registered Member

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    Sigh.....I'd help but I know only the absolute basics of trigonometry right now. :(
     
  22. sweater

    sweater Registered Member

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    [MOVE]I hate math!!![/MOVE]:mad:

    But, maybe you have to ask some of our scientists here...like...ohh I don't like to name names. :D
     
  23. NAMOR

    NAMOR Registered Member

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  24. WSFuser

    WSFuser Registered Member

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    i was able to confirm Blue's answer at another forum. anyways thanx all for ur help.
     
  25. Primrose

    Primrose Registered Member

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    When you get to DiffEq { DiffY'Q} (Differential Equations) next semester give me a buzz.:ninja:


    A kid called up his Mom from his college and asked her for some money, because he was broke.

    His Mother said, "Sure, sweetie. I will send you some money. You also left your calculus book here when you visited 2 weeks ago. Do you want me to send that up too?"

    "Uhh, oh yeah, o.k." responded the kid.

    So his Mom wrapped the book along with the checks up in a package, kissed Dad goodbye, and went to the post office to mail the money and the book. When she gets back, Dad asked, "Well how much did you give the boy this time?"

    "Oh, I wrote 2 checks, one for $20, and the other for $1,000 out to him."

    "That's $1020!!!" yelled Dad, "Are you crazyo_O"

    "Don't worry hon," Mom said, kissed Dad on the on top of his bald head, "I taped the $20 check to the cover of his book, but I put the $1,000 one somewhere between the pages in chapter 19!"


    Or you can DIY;)


    http://www.sosmath.com/
     
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