1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Goniometric equation

  1. Mar 3, 2013 #1
    1. The problem statement, all variables and given/known data
    sen(2x) * sen(x) = sen(4x) * sen(3x)

    3. The attempt at a solution
    I applied product to sum and sum to product identities and now I get cos(3x)=cos(7x ) how can I solve it?

    thank you
     
  2. jcsd
  3. Mar 3, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi scientifico! :smile:
    yup! :smile:

    so 3x = ±7x + … ? :wink:

    (alternatively, use the formula for cosA - cosB)
     
  4. Mar 3, 2013 #3
    What is this?
     
  5. Mar 3, 2013 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    draw the graph of cosθ …

    what has to be the relation between θ1 and θ2 if cosθ1 = cosθ2 ? :wink:
     
  6. Mar 3, 2013 #5
    θ1 = θ2 ?
     
  7. Mar 3, 2013 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    yes, but what are all the other solutions?

    (and have you drawn a graph of cosθ ?)
     
  8. Mar 4, 2013 #7
    Yes but i don't know what to search for
     
  9. Mar 4, 2013 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    If cos(3x) = cos(7x), then you have cos(7x) - cos(3x) = 0 .

    Use the sum to product identities to change this to the product of two sines .

    [itex]\displaystyle \cos \theta - \cos \varphi = -2\sin\left( {\theta + \varphi \over 2}\right) \sin\left({\theta - \varphi \over 2}\right)[/itex]

    It's almost always easier to solve an equation with product that equals zero than one with a sum/difference that equals zero.
     
  10. Mar 5, 2013 #9
    ok but that way I get cos(5x)
     
  11. Mar 5, 2013 #10

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    no, you get 2sin(5x)sin(2x) = 0 :confused:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Goniometric equation
  1. Quadratic Equation (Replies: 6)

  2. Trig equation (Replies: 10)

  3. Equation query (Replies: 4)

  4. Solving an equation (Replies: 4)

Loading...