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Thread: Surds

  1. #1 Surds 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Doe anyone know how to express sin10 in terms of surds??

    thanks


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  3. #2 Re: Surds 
    Forum Bachelors Degree x(x-y)'s Avatar
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    Quote Originally Posted by Heinsbergrelatz
    Doe anyone know how to express sin10 in terms of surds??

    thanks
    What do you need this for? If it's for a calculation needing an answer in exact form- then just leave it as sin10, or if it's for an answer- you can simply leave it as sin10 again. I hope that's what you're asking for...


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  4. #3  
    Forum Junior c186282's Avatar
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    You may be out of luck.
    I have look, tried a quick set of identities and looked on Wolfram Alpha and have not been able to find an expression for
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  5. #4 Re: Surds 
    Forum Masters Degree thyristor's Avatar
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    Quote Originally Posted by Heinsbergrelatz
    Doe anyone know how to express sin10 in terms of surds??

    thanks
    Is that 10 degrees or 10 radians?
    373 13231-mbm-13231 373
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  6. #5  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Man.. but does that necessarily mean that sin10 in surds does not exist? or still can be expressed?
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  7. #6  
    Forum Junior c186282's Avatar
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    I would not say it does not exist but it may not have been found yet. There may be a way to prove that it can not be written out in a closed form but I do no know how to do that.
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  8. #7  
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    If you can get sin10 in terms of sin30, you will have your answer (sin30 = 1/2).
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  9. #8  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Yea i kinda noticed that too, if you see my other post. Anyway i got the answer
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  10. #9  
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    Quote Originally Posted by Heinsbergrelatz
    Anyway i got the answer
    Post it here!
    What is
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  11. #10  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    okay its pretty ugly but here it is:



    i think i can represent every single angle of tan cos sin in terms of surds, even sin1. Maybe like not irrational numbers but i think i will try irrational angles next.
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  12. #11  
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    But You see i just do NOT get the imaginary unit...... what that represents in the surd.. i mean i know what complex numbers are, just i dont get it in this situation at all. Or maybe my surd is wrong.. Any corrections would be great if i am wrong.
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  13. #12  
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    I'm very surprised to see an in your result. We know that is real and therefore one must be able to simply what you have to give just a real number if it is correct.
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  14. #13  
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    I have taken this and evaluated it to get:

    0.173648177666930348851716626769314796000375677184 07
    and
    0.173648177666930348851716626769314796000375677184 07

    And to my surprise you seem to have it! Now we need to clean it up and get rid of that pesky

    Can you give and out line of your steps?

    P.S. Notice: I could not leave that in your expression I had to write it as . Yes I'm that picky.
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  15. #14  
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    I think I see how you have done this but...

    I do not think we can get rid of the nasty . I can simplify it down to:

    But because I can not get the complex part cleanly by itself I cannot cleanly write down the 1/3 root. And if I replace the exponent I get:

    Which now has the pesky in the solution.

    And if I "cleverly" solve this expression for I get the same form that I could not simplify.

    So I think your result is clever but not complete. I think to really satisfy your original question we need to get rid of all the 's and of course get the out of the answer.
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  16. #15 Re: Surds 
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    Quote Originally Posted by Heinsbergrelatz
    Doe anyone know how to express sin10 in terms of surds??

    thanks
    1 You cannot possibly mean sin(10). You must mean

    2.

    3. Letting and noting that we have

    or




    This equation has 3 real roots. While it is solvable by radicals, the radicals involve roots of complex numbers, which require knowledge of exact values of sines and cosines in order to be expressed in terms of "surds".
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  17. #16  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    yes of course 10 degrees.

    You see if i pose my workings its alittle hard with all the Tex symbols. But basically i had the trouble before because i wasn't entirely familiar with cubic functions. So 2 days ago i devoted some time to study only cubic functions, and its general applications, and voila, i managed to solve it using the general solution for x in a polynomial with n=3

    does anyone know how to erase the "i", in my sin10degrees??????
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  18. #17  
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    Quote Originally Posted by Heinsbergrelatz

    does anyone know how to erase the "i", in my sin10degrees??????
    That is the catch both "DrRocket" and I have come so the same conclusion. The solution that is obtained has the or written another way the in the answer.
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  19. #18  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    do you think its possible?? or maybe there is a whole other approach of getting it. I better try and think about it.
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  20. #19  
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    Quote Originally Posted by Heinsbergrelatz
    do you think its possible??
    I would guess No. But I do not have a proof that shows it is impossible. I would suggest that you do not spend any more time on this but remember it. You may find similar problems where you know the answer is real but you can't get the out.
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