Help with Multiple Angle Identities POSSIBLY HELP?

Discussion in 'Random Topic Center' started by OLD_SCHOOL_PLAYER, May 8, 2008.

  1. OLD_SCHOOL_PLAYER

    OLD_SCHOOL_PLAYER New Member

    Hi everyone, I am looking for some help on math. I looked the solution up in the back of the text book, but I am puzzled on how they are getting that answer. They showed their work but I am just curious on if I am interpreting it right and stuff.


    Here is the first problem:

    sin^4(x) = 1/8(3 - 4cos2x + cos4x)

    = (sin²x)² *I understand this

    = [1/2(1-cos2x)]² *I believe they substituted 1-cos²x for sin²x...and then to get rid of the ² on the cos, they took the square root of the equation, so they put times 1/2 instead. LMK if that is the correct way of thinking.

    = 1/4(1 - 2cos²x + cos²2x) *I think they foiled out (1-cos2x) (shown down below)

    FOILED:
    (1-cos2x) (1-cos2x)
    = 1 - cos2x - cos2x + cos²2x
    = 1 - 2cos2x + cos²2x

    = 1/4[1 - 2cos2x + 1/2(1 + cos4x)] *I don't know what happened here where the bold face is at.

    = 1/8(2 - 4cos2x + 1 + cos4x) *IDK

    = 1/8(3 - 4cos2x + cos 4x) *which is what we were trying to prove

    -----------------------------------------------------------------------------------------

    Second Problem: FINISHED TY TO ARMondak!
    Use half-angle identities to find all solutions in the interval [0, 2π)

    cos²x = sin²(x/2)

    answer:
    π/3, π, 5π/3

    *π = pi symbol just to lyk*

    I do not understand how to do this one, if someone can explain it would be mostly appreciated.

    Thank you for reading.
     
    Last edited: May 8, 2008
  2. ARMondak

    ARMondak New Member

    Take the right side and substitute ((1-cosx)/2)^1/2 for sin^2 x/2, keeping the square. The square and square root cancel out, leaving you with:

    cos^2 x = (1 - cos x)/2

    Then multiply both sides by 2

    2 cos^2 x = 1 - cos x

    Bring everything to the left

    2 cos^2 x + cos x - 1 = 0

    Factor

    (2 cos x - 1) (cos x + 1)

    Leaving

    cos x = 1/2, -1

    Which will give you

    x = 60 (n/3) and 240 (5n/3) when cos x = 1/2 and 180 (n) when cos x = -1

    Hope this helps.
     
  3. OLD_SCHOOL_PLAYER

    OLD_SCHOOL_PLAYER New Member

    I am so sorry but the first line lost me : /

    I understand what you do from there but I am a little confused on the first step and how you did it.
     
  4. bullados

    bullados <a href="http://pokegym.net/forums/showthread.php?

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