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Math Help - Find all answers given the following

  1. #1
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    Find all answers given the following

    for the following domain

    The steps that I used:
    cos(x+3) =1/5
    x+3 = cos-1 (1/5)
    x= cos-1(1/5) -3
    that gives me one of the answers


    for this cos-1(0.7)= x
    this gave me one of the answers

    How do I find the other answers
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  2. #2
    MHF Contributor
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    West Malaysia
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    Quote Originally Posted by midnightwynter View Post
    for the following domain

    The steps that I used:
    cos(x+3) =1/5
    x+3 = cos-1 (1/5)
    x= cos-1(1/5) -3
    that gives me one of the answers


    for this cos-1(0.7)= x
    this gave me one of the answers

    How do I find the other answers
    HI

    5\cos (x+3)=1

    \cos (x+3)=\frac{1}{5}

    cos is positive here so it must be in the first and fourth quadrant .

    x+3= 78.46 , 281.54

    x= 75.46 , 278.54 (in degrees)

    x= 1.317 , 4.861 (in radians)

    (b) \cos x=0.7

    again cos is positive (1st and 4th quadrant)

    x=0.795 , 5.488 , 7.078 , 11.77 (in radians)

    There are 2 extra solutions (red) because the domain goes up to 4 pi , which means another round . So just add 2pi to 0.795 and 5.488 respectively to get them .
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