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Math Help - URGENT HELP!!! lol (Trig Problems)

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    Exclamation URGENT HELP!!! lol (Trig Problems)

    1. (sinx/1+sinx) - (sinx/1-sinx)

    2. tanx(cotx-cosx) = ?

    3. cos4x

    4. (tanx+1)(2sinx-sqrt3) = 0

    5. sin2x + sinx = 0

    6. sin^2(2)x=1

    If yall could help me that would be great, i really just kinda suck at all of this, im more of a visual learner if you get what im saying.
    Last edited by math/retarded; May 3rd 2009 at 04:46 PM.
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    Quote Originally Posted by math/retarded View Post
    1. (sin/1+sin) - (sin/1-sin)

    2. tan(cot-cos) = ?

    3. cos4

    4. (tanx+1)(2sinx-sqrt3) = 0

    5. sin2x + sinx = 0

    6. sin^2(2)x=1

    If yall could help me that would be great, i really just kinda suck at all of this, im more of a visual learner if you get what im saying.
    A lot of what you've posted is nonsense, because \sin, \cos, \tan, \cot, \csc, \sec have no meaning unless you have a number or variable attached.

    Also, you haven't specified what you wanted to do with these equations.

    I'm assuming for 1 and 2, you're using identites to simplify, and for 4, 5, 6, you're solving the equations.

    1. \frac{\sin{x}}{1 + \sin{x}} - \frac{\sin{x}}{1 - \sin{x}}.

    Here multiply the top and bottom of each term by a cleverly disguised 1.

    = \frac{\sin{x}}{1 + \sin{x}}\times \frac{1 - \sin{x}}{1 - \sin{x}} - \frac{\sin{x}}{1 - \sin{x}}\times \frac{1 + \sin{x}}{1 + \sin{x}}

     = \frac{\sin{x}(1 - \sin{x})}{(1 + \sin{x})(1 - \sin{x})} - \frac{\sin{x}(1 + \sin{x})}{(1 - \sin{x})(1 + \sin{x})}

     = \frac{\sin{x} - \sin^2{x}}{1 - \sin^2{x}} - \frac{\sin{x} +\sin^2{x}}{1 - \sin^2{x}}

     = \frac{\sin{x} - \sin^2{x} - \sin{x} - \sin^2{x}}{1 - \sin^2{x}}

     = -\frac{2\sin^2{x}}{\cos^2{x}}

     = -2\tan^2{x}.
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    Quote Originally Posted by math/retarded View Post
    1. (sin/1+sin) - (sin/1-sin)

    2. tan(cot-cos) = ?

    3. cos4

    4. (tanx+1)(2sinx-sqrt3) = 0

    5. sin2x + sinx = 0

    6. sin^2(2)x=1

    If yall could help me that would be great, i really just kinda suck at all of this, im more of a visual learner if you get what im saying.
    2. \tan{x}(\cot{x} - \cos{x}) = \frac{\sin{x}}{\cos{x}}\left(\frac{\cos{x}}{\sin{x  }} - \cos{x}\right)

     = 1 - \sin{x}.



    3. Just put it into the calculator.



    4. (\tan{x} + 1)(2\sin{x} - \sqrt{3}) = 0

    By the null factor law \tan{x} + 1 = 0 or 2\sin{x} - \sqrt{3} = 0.


    Case 1: \tan{x} + 1 = 0

    \tan{x} = -1

    x = \left\{\pi - \frac{\pi}{4}, 2\pi - \frac{\pi}{4}\right\} + 2\pi n, n \in \mathbf{Z}

    x = \left\{\frac{3\pi}{4}, \frac{7\pi}{4}\right\} + 2\pi n, n\in \mathbf{Z}.


    Case 2: 2\sin{x} - \sqrt{3} = 0

    2\sin{x} = \sqrt{3}

    \sin{x} = \frac{\sqrt{3}}{2}

    x = \left\{\frac{\pi}{3}, \pi - \frac{\pi}{3}\right\} + 2\pi n, n \in \mathbf{Z}

    x = \left\{\frac{\pi}{3}, \frac{2\pi}{3}\right\} + 2\pi n, n \in \mathbf{Z}.


    So putting them together

    x = \left\{ \frac{\pi}{3}, \frac{3\pi}{4}, \frac{2\pi}{3}, \frac{7\pi}{4}\right\} + 2\pi n, n \in \mathbf{Z}.
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    Quote Originally Posted by math/retarded View Post
    1. (sinx/1+sinx) - (sinx/1-sinx)

    2. tanx(cotx-cosx) = ?

    3. cos4x

    4. (tanx+1)(2sinx-sqrt3) = 0

    5. sin2x + sinx = 0

    6. sin^2(2)x=1

    If yall could help me that would be great, i really just kinda suck at all of this, im more of a visual learner if you get what im saying.
    5. \sin{(2x)} + \sin{x} = 0

    2\sin{x}\cos{x} + \sin{x} = 0

    \sin{x}(2\cos{x} + 1) = 0

    Can you go from here?


    6. \sin^2{(2x)} = 1

    \sin{(2x)} = \pm 1.

    Can you go from here?
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