Results 1 to 4 of 4

Math Help - Reducing a trig equation

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    97

    Reducing a trig equation

    Hi
    I am trying to solve this but cant get it in one/two trig ratios

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2010
    Posts
    17
    Quote Originally Posted by 200001 View Post
    Hi
    I am trying to solve this but cant get it in one/two trig ratios

    \sin\phi(\cos \phi + \frac{1}{\sin\phi}) = \sin\phi(\frac{\cos\phi \sin\phi + 1}{\sin\phi}) = \cos\phi \sin\phi + 1 = \cos\phi \sin\phi + \cos^2\phi + \sin^2\phi

    Than:
    \cos\phi \sin\phi + \cos^2\phi + \sin^2\phi = 2\cos^2\phi
    \cos\phi \sin\phi + \sin^2\phi = \cos^2\phi
    \cos\phi \sin\phi  = \cos^2\phi - \sin^2\phi
    \cos\phi \sin\phi  = \cos2\phi
    \frac{1}{2} \sin2\phi  = \cos2\phi

    I hope, you will now easier find the solution of trig. equ.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,073
    Thanks
    301
    Try this:
     <br />
sin(\theta) (cos(\theta) + csc(\theta)) = sin(\theta) (cos(\theta) + 1/sin(\theta)) = sin(\theta) cos(\theta) + 1 = 2cos^2(\theta)<br />

    <br />
sin(\theta)cos(\theta) = 2 cos^2(\theta) -1<br />

    Square both sides:
    <br />
sin^2(\theta) cos^2(\theta) = 4 cos^4(\theta) - 4 cos^2 (\theta) + 1<br />

    Substitute  sin^2 \theta = 1 - cos^2 \theta :

    <br />
(1 - cos^2(\theta))*cos^2 (\theta) = 4 cos^4(\theta) - 4 cos^2 (\theta) + 1<br />

    <br />
5 cos^4(\theta) -5cos^2(\theta) +1 = 0<br />

    Let  \alpha = cos^2(\theta):
     <br />
5 \alpha^2 - 5 \alpha + 1 = 0<br />

    Solve using the quadratic formula:
     <br />
\alpha = \frac 1 2 \pm \frac {\sqrt {5}}{10}<br />
    <br />
cos(\theta) = \pm \sqrt { \frac 1 2 \pm \frac {\sqrt {5}}{10} }<br />
    <br />
\theta = Arccos \left (\pm \sqrt { \frac 1 2 \pm \frac {\sqrt {5}}{10}} \right )<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2009
    Posts
    97
    Brilliant
    thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Reducing to 2D heat equation
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: April 20th 2010, 11:06 AM
  2. Reducing to a linear equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: January 26th 2010, 04:00 PM
  3. reducing trig functions to a single function
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 12th 2009, 06:44 AM
  4. Reducing Quadratic Surface Equation, HELP!
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 11th 2009, 09:33 AM
  5. Analalitic geometry- reducing Equation
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: August 14th 2007, 09:23 AM

Search Tags


/mathhelpforum @mathhelpforum