Results 1 to 8 of 8

Math Help - Sinister Sine

  1. #1
    Junior Member
    Joined
    Nov 2008
    From
    Far away.
    Posts
    47

    Smile Sinister Sine

    I've tried to solve the equation 2cos^2x= sin 2x for 0 < x < pi

    I know I have to express it in either sine or cos. And after that substitute by t and solve the quadratic equation. But I must be doing something wrong, because I keep getting the wrong I answer.
    I would appreciate if you could solve and explain to me how it's solved

    Thanks a lot,
    Amine.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2007
    Posts
    329
    Is 2\cos^2x= \sin 2x your equation ? If so then \cos^2x-\cos x\sin x=0 using the \sin 2x=2\sin x\cos x identity. So you have to solve \cos x(\cos x-\sin x)=0 therefore \cos x=0\Rightarrow x=k\pi \text{ and }\frac 32\pi and \sin x=\cos x\Rightarrow x=\pi /4.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    2 \cos^2x= \sin 2x

    2 \cos^2x= 2 \sin x \cos x

    \cos x - \sin x) = 0" alt="2 \cos x \\cos x - \sin x) = 0" />

    A product is equal to 0 if at least one of the terms is equal to 0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2008
    From
    Far away.
    Posts
    47
    Ok, so I actually don't need to substitute with t?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by Aminekhadir View Post
    Ok, so I actually don't need to substitute with t?
    What is t ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Nov 2008
    From
    Far away.
    Posts
    47
    It's like t = sin x

    For example:
    3 sin^2(x) = 1 - sin^2(x)
    and it becomes
    3 t^2 = 1 - t^2

    But this is where I get very confused, because we have cos in our equation and not sine? I hope I haven't confused you also. I'm sorry for that.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Using t = sin x is not a general rule to solve trig equation
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Nov 2008
    From
    Far away.
    Posts
    47
    Ok, thanks a lot for the help! I think I have confused myself too much by complicating it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sine Law
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 3rd 2010, 03:50 PM
  2. The Sinister Sine Function
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 26th 2009, 02:43 AM
  3. Sine
    Posted in the Trigonometry Forum
    Replies: 17
    Last Post: January 26th 2009, 12:14 AM
  4. help with sine
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 11th 2007, 12:31 AM
  5. Law of Sine
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 13th 2005, 09:06 AM

Search Tags


/mathhelpforum @mathhelpforum