Results 1 to 5 of 5

Math Help - Fundamental identities

  1. #1
    Member >_<SHY_GUY>_<'s Avatar
    Joined
    Jan 2008
    From
    CA
    Posts
    181

    Question Fundamental identities

    CAn someone explain how you get from:

    sinx cosx^2 - sinx to sinx (cos^2x-1) to -sinx (1-cos^2x) to -sinx( sin^2x) to -sin^3x

    and help me with factoring this equation:

    sec^3x-sec^2x-secx+1

    Thank you in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    {\color{blue}\sin x} \cos^{2} x - {\color{blue}\sin x}
    = {\color{blue}\sin x} \left(\cos^{2} x - 1\right)

    sin x was factored out of the expression just as you would if you had something like ab + a = a(b + 1)

    = -\sin x \left(1 - cos^{2} x\right) (-1 was factored out of the bracketed expression)

    Recall that: \cos^{2} x + \sin^{2} x = 1 \: \Rightarrow \: {\color{red}\sin^{2}x = 1 - \cos^{2} x}

    Substituting it in, we get:
    = -\sin x \cdot {\color{red} \sin^{2} x}
     = -\sin^{3} x since a^{m}a^{n} = a^{m+n}

    ----------------------------
    {\color{red}\sec^{3} x - \sec^{2} x} \: {\color{blue}- \sec x + 1}

    Focusing on the red, let's factor out \sec^{2} x and for the blue, let's factor out -1:
    = \sec^{2} x (\sec x - 1) -( \sec x - 1)

    Factor out (sec x - 1):
    = (\sec x - 1){\color{magenta}\left(sec^{2}x - 1\right)}

    And hopefully the expression in purple reminds you of a certain identity.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member >_<SHY_GUY>_<'s Avatar
    Joined
    Jan 2008
    From
    CA
    Posts
    181
    so from that i use the pythagorean identities multiply, and thats it right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    I'm not sure what you mean by what you wrote. What I was referring to was this identity: 1 + \tan^{2} x = \sec^{2} x
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member >_<SHY_GUY>_<'s Avatar
    Joined
    Jan 2008
    From
    CA
    Posts
    181
    which is derived from the pythagorean identity: sin^2+cos^2 = 1
    and from there you multiply
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fundamental Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 2nd 2010, 03:25 PM
  2. calc fundamental identities
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 11th 2010, 08:19 AM
  3. Fundamental identities to simplify
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 21st 2010, 12:12 AM
  4. Using Fundamental Identities
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 4th 2009, 10:48 AM
  5. Finding asymptotes+Fundamental identities
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 25th 2009, 11:30 AM

Search Tags


/mathhelpforum @mathhelpforum