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Math Help - Trigonometric equations?

  1. #1
    Super Member fardeen_gen's Avatar
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    Trigonometric equations?

    The number of solutions of tan(5π cos θ) = cot (5π sin θ) in (0,2π) is?
    A) 28
    B) 14
    C) 4
    D) 2
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by fardeen_gen View Post
    The number of solutions of tan(5π cos θ) = cot (5π sin θ) in (0,2π) is?
    A) 28
    B) 14
    C) 4
    D) 2
    Personally, I would graph it. And then you can count the number of times f(x)=\tan(5\pi\cos(\theta))-\cot(5\pi\sin(\theta))
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  3. #3
    Super Member fardeen_gen's Avatar
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    No analytical method to solve this? In the case i go in for a graph, can u suggest the name of any good graphing calculator online?

    Thanks.
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by fardeen_gen View Post
    The number of solutions of tan(5π cos θ) = cot (5π sin θ) in (0,2π) is?
    This equality can be written

    \frac{\sin(5\pi\cos\theta)}{\cos(5\pi\cos\theta)}-\frac{\cos(5\pi\sin\theta)}{\sin(5\pi\sin\theta)}=  0

    If \sin(5\pi\sin\theta)\neq 0 and \cos(5\pi\cos\theta)\neq 0, this equation is the same as  \sin(5\pi\cos\theta)\sin(5\pi\sin\theta)- \cos(5\pi\sin\theta)\cos(5\pi\cos\theta)=0<br />

    Since \cos(a+b)=\cos a \cos b-\sin a\sin b the equation becomes \cos\left[5\pi(\sin \theta+\cos \theta) \right]=0.

    EDIT : To find the number of solutions you may need \sin \theta + \cos \theta = \sqrt{2}\cos\left(\theta-\frac{\pi}{4}\right).
    Last edited by flyingsquirrel; June 22nd 2008 at 10:08 AM.
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