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!

Homework Help: Solving trigonometric equations

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    How do you solve cosx=-cos2x?

    3. The attempt at a solution
    I've tried graphing it, but just wasn't able to crack the solutions

    Thanks for help!
  2. jcsd
  3. Oct 9, 2011 #2


    User Avatar
    Homework Helper

    What is the relation between two angles a and b if cos(a)=-cos(b)? Look at the unit circle.

    Or use the formula cos(2x)=cos^(x)-sin^2(x)

  4. Oct 9, 2011 #3
    If you merely want the answer (without proof), type "solve cos(x)=-cos(2x) for x" in wolfram alpha. If you want to figure out the proof, look up the trig formula that lets you express cos(2x) in terms of cos(x). With that substitution, you will have transformed your equation into a quadratic equation, with cos(x) as the unknown, the solution of which is cos(x)=-1 (implying x=-pi) or cos(x)=1/2 (implying x=pi/3 or x=-pi/3). Of course, add any integer multiple of 2pi to these answers to characterize the infinite number of solutions.
  5. Oct 9, 2011 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    or use cos(2x) = 2cos2(x) - 1
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook