1. Limited time only! Sign up for a free 30min personal 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!

How to solve this trig equation

  1. Aug 22, 2012 #1

    lo2

    User Avatar

    1. The problem statement, all variables and given/known data

    Solve this equation:

    [itex]cos^2(2x)=0,36[/itex]

    For [itex]x \in [-\pi;\pi][/itex]


    2. Relevant equations

    -

    3. The attempt at a solution


    [itex]cos^2(2x)=0,36 \Leftrightarrow cos(2x)=\sqrt{0,36} \Leftrightarrow 2x=cos^{-1}(\sqrt{0,36}) [/itex]

    And then I am not sure exactly how to proceed... When should I put in the [itex] 2p \pi [/itex] where [itex] x \in Z [/itex], to get all of the possible solutions?
     
    Last edited: Aug 22, 2012
  2. jcsd
  3. Aug 22, 2012 #2

    Mark44

    Staff: Mentor

    Not true. cos(2x) can also be negative. In your second equation, you took the square root of the right side, but not the left side.
    Also, you should simplify √(.36).

     
  4. Aug 22, 2012 #3

    lo2

    User Avatar

    I corrected the mistake about not taking the square root on either side. So you mean I should put ± in front of the square root?
     
  5. Aug 22, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes, use the ± .
     
  6. Aug 22, 2012 #5

    Mark44

    Staff: Mentor

    The domain for x is restricted to [##-\pi, \pi##], so you're going to get only a handful of solutions.
     
  7. Aug 23, 2012 #6

    lo2

    User Avatar

    Ok I have come up with this solution:

    [itex]\frac{cos^{-1}(\pm \sqrt{0,36})}{2}+p\pi[/itex]

    Where the solutions are: [itex]cos^{-1}(\sqrt{0,36})-\pi, cos^{-1}(-\sqrt{0,36}), cos^{-1}(\sqrt{0,36}), cos^{-1}(-\sqrt{0,36})+\pi[/itex]

    Since the solutions have to be in the interval of -pi to pi.
     
  8. Aug 23, 2012 #7

    Mark44

    Staff: Mentor

    Why do you keep writing √(.36)? That simplifies to an exact value. What is this value?

    I think you would be better off by NOT using cos-1, since that will give you only one value. I would sketch a graph of y = cos(2x) on the interval [##-2\pi, 2\pi##] (since x ##\in## [##-\pi, \pi##]), and identify all of the points at which cos(2x) = ±B, where B is the simplified value of √(.36).

    EDIT: Also, your work above suggests that there are four solutions. I get quite a few more than that.
     
    Last edited: Aug 23, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to solve this trig equation
  1. Solving trig equations (Replies: 14)

Loading...