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Math Help - cos5x=0 waaaaaaaaaaaaah

  1. #1
    Member i_zz_y_ill's Avatar
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    cos5x=0 waaaaaaaaaaaaah

    could someone explain this working,makes no sense to me,Q is solve sin5x=0 in range 0 to 2pie inclusive, giving roots as ,multiples of pi

    sin5x=0 implies 5x=kpie , k=0 to 9
    implies x=kpie/5 therefore k=0 to9

    i dont have a clue about this does sum 1 know???
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  2. #2
    Moo
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    A Cute Angle Moo's Avatar
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    Hello,

    sin5x=0 implies 5x=kpie , k=0 to 9
    implies x=kpie/5 therefore k=0 to9
    I don't understand your writing, though the result is (almost) correct. But the "therefore" part makes no sense...

    Let X=5x. Then X is between 0 and 10 pi.
    So you have to solve for sin(X)=0

    As you said, X=k*pi, with k=..., -2, -1, 0, 1, 2, ....

    Since X is between 0 and 10 pi, therefore k=0, 1, ..., 9, 10 (0 and 2 pi are inclusive).

    Solutions are X=0, \ \pi, \ 2 \pi, \dots , \ 9 \pi, \ 10 \pi

    ---> x=0, \frac{\pi}{5}, \frac{2 \pi}{5}, \dots , \frac{9 \pi}{5}, 2 \pi

    Is it ok ? oO
    Last edited by Moo; May 4th 2008 at 07:16 AM. Reason: typo
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,



    I don't understand your writing, though the result is correct. But this implication makes no sense...

    Let X=5x. Then X is between 0 and 10 pi.
    So you have to solve for sin(X)=0

    As you said, X=k*pi, with k=..., -2, -1, 0, 1, 2, ....

    Since X is between 0 and 10 pi, therefore k=0, 1, ..., 9, 10 (0 and 2 pi are inclusive).

    Solutions are X=0, \ \pi, \ 2 \pi, \dots , \ 9 \pi, \ 10 \pi

    ---> x=0, \frac{\pi}{5}, \frac{2 \pi}{5}, \dots , \frac{9 \pi}{5}, 10 \pi

    Is it ok ? oO
    Last one should be \frac{10\pi}{5}

    Right? Probably just a typo.
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  4. #4
    Senior Member Peritus's Avatar
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    first of all try to give a meaningful title to your post instead of :

    and avoid using chat language such as:
    does sum 1 know
    ------------------------------------------------------------------------


    \begin{gathered}<br />
  \sin 5x = 0 \hfill \\<br />
   \Leftrightarrow 5x = \pi k,\quad k \in Z \hfill \\<br />
   \Leftrightarrow x = \frac{\pi }<br />
{5}k \hfill \\ <br />
\end{gathered} <br />

    now we are interested in the answers which are in the following interval [0, 2pi]:


    \begin{gathered}<br />
  0 \leqslant \frac{\pi }<br />
{5}k \leqslant 2\pi  \hfill \\<br />
   \hfill \\<br />
   \leftrightarrow 0 \leqslant k \leqslant 10 \hfill \\ <br />
\end{gathered}
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