Results 1 to 3 of 3

Math Help - Find solutions of an equation within an interval

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    2

    Unhappy Find solutions of an equation within an interval

    My class has moved on to a new section of trigonometry that I am stuck on.

    I am suppose to find all solutions of the equation in the interval [0,2π]

    An example problem that is in my text book has a problem with its corresponding answer below, but I don't really follow.

    Example: cosł x = cos x
    Answer: 0, π/2, π, 3π/2

    It would be really helpful if you can explain the steps that you take in order to get the final answer.

    Also π = pi.

    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by root View Post
    My class has moved on to a new section of trigonometry that I am stuck on.

    I am suppose to find all solutions of the equation in the interval [0,2π]

    An example problem that is in my text book has a problem with its corresponding answer below, but I don't really follow.

    Example: cosł x = cos x
    Answer: 0, π/2, π, 3π/2

    It would be really helpful if you can explain the steps that you take in order to get the final answer.

    Also π = pi.

    Thanks in advance
    If you subtract cosine from both sides you get

    \cos^3(x)-\cos(x)=0

    Now factor the left hand side completely to get

    \cos(x)[\cos^2(x)-1]=0 \iff \cos(x)[\cos(x)-1][\cos(x)+1]=0

    The last step comes from the difference of squares.

    Now use the zero factor principle to set each factor equal to zero and solve.

    \cos(x)=0 \quad \cos(x)-1=0\quad \cos(x)+1=0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    2

    Thank you

    Thank you for replying so quickly. Your explanation was a lot more helpful than my textbook's. I get it now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 5th 2010, 09:03 PM
  2. find all solutions in the interval of [0, and 2pi)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 27th 2009, 01:47 PM
  3. Find all solutions of the Equation
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 27th 2008, 07:58 PM
  4. find solutions in eqautions in interval
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 21st 2008, 11:23 AM
  5. Find all solutions in the interval..........
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 19th 2008, 08:26 AM

Search Tags


/mathhelpforum @mathhelpforum