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Math Help - Trigonometric Equations

  1. #1
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    Trigonometric Equations

    Hi. I need help to find the:
    -Amplitude
    -Period
    -Vertical Shift
    -Horizontal Shift

    1) y= 2sin(4x+pi)+3
    2) y= -3cos((x/2)+2pi)-5

    Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by takuto View Post
    Hi. I need help to find the:
    -Amplitude
    -Period
    -Vertical Shift
    -Horizontal Shift

    1) y= 2sin(4x+pi)+3
    2) y= -3cos((x/2)+2pi)-5

    Any help would be greatly appreciated.
    y = A\cos[B(x + C)] + D ... also sine

    |A| = amplitude

    period = \frac{2\pi}{|B|}

    C = horizontal shift ... (+) left , (-) right

    D = vertical shift ... (+) up , (-) down
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  3. #3
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    Quote Originally Posted by skeeter View Post
    y = A\cos[B(x + C)] + D ... also sine

    |A| = amplitude

    period = \frac{2\pi}{|B|}

    C = horizontal shift ... (+) left , (-) right

    D = vertical shift ... (+) up , (-) down
    I was wondering if I did it right:
    2sin[4x+pi]+3
    A=2
    B=pi/2
    C=pi/4
    D=3

    -3cos((x/2)+2pi))-5
    A=-3
    B=4pi
    C=0
    D=-5
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  4. #4
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    Quote Originally Posted by takuto View Post
    I was wondering if I did it right:
    2sin[4x+pi]+3
    A=2
    B=pi/2
    C=pi/4
    D=3

    -3cos((x/2)+2pi))-5
    A=-3
    B=4pi
    C=0
    D=-5
    no
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  5. #5
    Junior Member
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    Quote Originally Posted by takuto View Post
    I was wondering if I did it right:
    2sin[4x+pi]+3
    A=2
    B=pi/2
    C=pi/4
    D=3

    -3cos((x/2)+2pi))-5
    A=-3
    B=4pi
    C=0
    D=-5
    a few things to remember

    Amplitude is never negative (it's an absolute value)
    the period of a sin and cos is 2pi / B. Same for sec and csc,
    vertical shift is the number that's outside (you got that right in these cases)
    horizontal shift is -C/B if I'm not mistaken.
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  6. #6
    Senior Member pacman's Avatar
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    here is the graph of the two trigonometric equations, try to figure out the answer by inspection . . .
    Attached Thumbnails Attached Thumbnails Trigonometric Equations-qa.gif   Trigonometric Equations-qz.gif  
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