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Thread: x=pi/2 is a solution?

  1. #1
    woo
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    x=pi/2 is a solution?

    Solve 2/(\cot {x}) + 3/(\csc {x}) = 0, 0<x<2\pi.

    After a few steps, I obtained

    (\sin {x})(2+3 \cos [x}) = 0

    \sin {x} = 0 or \cos {x} = -2/3

    From \sin {x} = 0, I obtained the solution x=\pi/2. Is x=\pi/2 is a solution?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: x=pi/2 is a solution?

    Quote Originally Posted by woo View Post
    Solve 2/(\cot {x}) + 3/(\csc {x}) = 0, 0<x<2\pi.

    After a few steps, I obtained

    (\sin {x})(2+3 \cos [x}) = 0

    \sin {x} = 0 or \cos {x} = -2/3

    From \sin {x} = 0, I obtained the solution x=\pi/2. Is x=\pi/2 is a solution?
    Hints:
    1. Look at the first term in the original equation.
    2. What is csc(0)?
    3. Is x = 0 permitted in the original equation?

    -Dan
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  3. #3
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    Re: x=pi/2 is a solution?

    Quote Originally Posted by woo View Post
    Solve 2/(\cot {x}) + 3/(\csc {x}) = 0, 0<x<2\pi.
    After a few steps, I obtained (\sin {x})(2+3 \cos [x}) = 0
    \sin {x} = 0 or \cos {x} = -2/3
    From \sin {x} = 0, I obtained the solution x=\pi/2. Is x=\pi/2 is a solution?
    Did you even bother to look at the graph?
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  4. #4
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    Re: x=pi/2 is a solution?

    $\sin{x} = 0 \implies x = k\pi$, which are not valid solutions.

    the Wolfram graph does not show the point discontinuities on the x-axis at integer multiples of $\pi$

    The valid solutions are where $x = \arccos\left(-\dfrac{2}{3}\right)$
    Attached Thumbnails Attached Thumbnails x=pi/2 is a solution?-trig_graf1.jpg   x=pi/2 is a solution?-trig_graf2.png  
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  5. #5
    woo
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    Re: x=pi/2 is a solution?

    Thanks a lot.
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