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: Trig transformation Question

  1. Apr 8, 2007 #1
    The question is "Solve each equation for exact solutions over the interval of [0,2pi).

    Equation: sin x = sin 2x

    I transformed the equation to

    sin x = 2sin x cos x

    then

    sin x/2sin x = cos x

    cos x = 1/2

    Answer: pi/3, 5pi/3

    but the book also has the answers 0, pi.

    What must I do to find the other two solutions?
     
  2. jcsd
  3. Apr 8, 2007 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You ASSUMED that sin(x) was non-zero when you divided with it, since you can't divide by zero.

    Since we see that the equation is ALSO fulfilled in the case sin(x)=0
    (The equation reduces then to 0=2*0*cos(x) which is always true),

    then the solutions of sin(x)=0 are also solutions of the original equation.
    Guess what those numbers might be..:smile:
     
  4. Apr 8, 2007 #3
    Thanks for the explanation. :)

    *edit* Figured it out now.
     
    Last edited: Apr 8, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook