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. Equation

  1. Mar 19, 2014 #1
    1. The problem statement, all variables and given/known data

    (sin(2x)) * (2sin(2x)-1)=0

    2. The attempt at a solution

    sin (2x) = 0

    x= 0, π

    sin (2x) = 1/2
    sinx = 1/4
    x = π/12 ; 11π/12

    There are two more solutions but I cannot seem to find them.
  2. jcsd
  3. Mar 19, 2014 #2


    User Avatar
    Science Advisor

    Are you to find x in the interval [itex]0\le x< 2\pi[/itex]? It would be better if you would tell us that!
    Yes, sin(x)= 0 for x= 0 and [itex]x= \pi[/itex].

    For 2 sin(2x)- 1= 0, yes, that leads to sin(2x)= 1/2.
    But you cannot then declare that sin(x)= 1/4!!
    The "2" is inside the function- you cannot divide by 2 until after you have removed the sine.
    (That's a howler of an error! I really hope that was carelessness.)

    From sin(2x)= 1/2 you get [itex]2x= \pi/6, \pi= \pi/6= 5\pi/6, 2\pi+ \pi/6= 13\pi/6, 3\pi- \pi/6= 17\pi/6[/itex]

    Notice that I have gone to 0 to [itex]2\pi[/itex] because I am going to divide by 2:

    [itex]x= \pi/12[/itex], [itex]x= 5\pi/12[/itex], [itex]13\pi/12[/itex], [itex]17\pi/12[/itex].
  4. Mar 19, 2014 #3
    My teacher had told me that I could remove the two from sin(2x) right away... sorry about that.

    From the sin(2x) = pi/6 ... i am kind of lost

    I know how you got pi/6, but the rest, I don't quite understand.
  5. Mar 19, 2014 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I hope that what your teacher means is that if you have sin(2x) = 0, then setting y = 2x you have sin(y) = 0, NOT sin(x) = 0. In fact, if sin(2x) = 0 then sin(x) is as far from 0 as the 'sin' can get: we would have either sin(x) = +1 or sin(x) = -1.

    Also, what you wrote above makes no sense: you do not have sin(2x) = pi/6; you do have sin(2x) = 1/2 = sin(pi/6), so 2x = pi/6.
    Last edited: Mar 19, 2014
  6. Mar 19, 2014 #5
    Yes, I meant to write 2x = pi/6 not sin 2x = pi/6
  7. Mar 19, 2014 #6
    I mainly don't understand the part where HallsOfIvy wrote pi = pi/6 = 5pi / 6 ...

    Where did he get the pi = pi/6 = 5pi / 6 ... from?
  8. Mar 19, 2014 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    That is NOT what he wrote. Read it again.

    He is just listing the several possible values of x, so what he wrote is shorthand for x = 0 or x = pi/6 or x = 5pi/6 or .... . He is not saying those values are equal to each other.
  9. Mar 19, 2014 #8


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I believe Halls meant to write

    From sin(2x)= 1/2 you get [itex]2x= \pi/6,\ \pi- \pi/6= 5\pi/6,\ 2\pi+ \pi/6= 13\pi/6,\ 3\pi- \pi/6= 17\pi/6\ .[/itex]

    in particular, [itex]\ ... \pi- \pi/6= 5\pi/6,\ ...[/itex]
  10. Mar 20, 2014 #9
    Yes. I have understood the problem.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted