Results 1 to 2 of 2

Thread: tanxsinx = 3sinx - secx

  1. #1
    Member
    Joined
    Dec 2008
    From
    Australia
    Posts
    161

    tanxsinx = 3sinx - secx

    Solve for x:

    equal to or less than 360
    equal to or more than 0

    tanxsinx = 3sinx - secx

    A problem I have been struggling with for ages.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    Quote Originally Posted by differentiate View Post
    Solve for x:

    equal to or less than 360
    equal to or more than 0

    tanxsinx = 3sinx - secx

    A problem I have been struggling with for ages.
    not very nice, I agree.

    $\displaystyle
    \tan{x}\sin{x} = 3\sin{x} - \sec{x}
    $

    $\displaystyle \frac{\sin{x}}{\cos{x}} \cdot \sin{x} = 3\sin{x} - \frac{1}{\cos{x}}$

    $\displaystyle \frac{\sin^2{x}}{\cos{x}} = \frac{3\sin{x}\cos{x} - 1}{\cos{x}}$

    $\displaystyle
    \sin^2{x} = 3\sin{x}\cos{x} - 1
    $

    $\displaystyle \sin^2{x} = 3\sin{x}\cos{x} - (\sin^2{x} + \cos^2{x})$

    $\displaystyle
    2\sin^2{x} - 3\sin{x}\cos{x} + \cos^2{x} = 0
    $

    $\displaystyle
    (2\sin{x} - \cos{x})(\sin{x} - \cos{x}) = 0
    $

    $\displaystyle 2\sin{x} = \cos{x}$ or $\displaystyle \sin{x} = \cos{x}$

    for $\displaystyle \sin{x} = \cos{x}$ ...

    $\displaystyle x = 45^{\circ}$ , $\displaystyle x = 225^{\circ}$

    for $\displaystyle 2\sin{x} = \cos{x}$

    $\displaystyle 4\sin^2{x} = cos^2{x}$

    $\displaystyle
    4\sin^2{x} = 1 - \sin^2{x}
    $

    $\displaystyle
    5\sin^2{x} - 1 = 0
    $

    $\displaystyle
    \sin^2{x} = \frac{1}{5}
    $

    $\displaystyle
    \sin{x} = \pm \sqrt{\frac{1}{5}}
    $

    the solutions to this part were found using a calculator and looking at a graph ...

    $\displaystyle x = \arcsin\left(\sqrt{\frac{1}{5}}\right)$

    and

    $\displaystyle
    x = \arcsin\left(\sqrt{\frac{1}{5}}\right) + 180^{\circ}
    $
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solve equation tanx=3sinx
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Dec 13th 2009, 08:56 AM
  2. Simplifying sin(x+4)secx?
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Mar 2nd 2009, 06:38 AM
  3. integrate (secx)^4
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jun 15th 2008, 06:11 AM
  4. differentia secx????????
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 3rd 2008, 05:42 AM
  5. The reciprocal of secx
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Apr 12th 2008, 07:30 PM

Search Tags


/mathhelpforum @mathhelpforum