1. Not finding help here? Sign up for a free 30min 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!

Writing A Trig Expression as an Algebraic Expression

  1. Jun 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Write the Trigonometric Expression as an algebraic expression.

    cos(2arccos 2x)

    2. Relevant equations

    Probably the inverse properties, I'm not sure.

    3. The attempt at a solution

    I know I can rewrite this equation as.

    u= arccos 2x

    cos(2cos u=2x)

    I can also say that the adjacent leg is 2x units long and the hypotenuse is 1 unit long. Then using the pythagorean theorm I can figure the opposite leg to be sqrt(1-4x2)

    I'm not sure If this is necessary though can someone point me in the right direction? The 2 in front of the arccos is throwing me off because if that wasn't there I would just use the inverse property and cos(arccos 2x) would equal 2x.
     
  2. jcsd
  3. Jun 18, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    If u=cos-1(2x) then you want to find cos(2u).

    cos(2u)=cos2u-sin2u=2cos2u-1 = 1-2sin2u

    and cos2u = (cosu)2
     
  4. Jun 18, 2010 #3
    I'm not sure I understand why you'd want to find cos(2u)

    The answer is supposed to be 8x2-1 and thats the answer listed in the back of the book.
     
  5. Jun 18, 2010 #4

    rock.freak667

    User Avatar
    Homework Helper

    cos(2cos-1(2x))

    if you put u = cos-1(2x), wouldn't cos(2cos-1(2x)) become cos(2u)?
     
  6. Jun 18, 2010 #5
    Thanks, now I understand.

    Once you have simplified it to 2cos2u-1 all you have to do is simplify it with the u in place

    cos2(arcsin 2x)=2x

    2(2x)2-1

    8x2-1

    Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Writing A Trig Expression as an Algebraic Expression
  1. Algebraic Expression (Replies: 4)

Loading...