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Thread: Determining a sinusoidal function from its graph, can amplitude be negative?

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    Determining a sinusoidal function from its graph, can amplitude be negative?

    I have two questions. A lot of the sources I have read say that amplitude cannot be negative, because it is a distance, and we take the absolute value of distance. However, other sources say that A can be negative (like SymboLab).

    My second question is, I have to find a function from its graph:

    I

    I first calculated the amplitude to be: (Max+Min) / 2 = (2+2) / 2 = 2

    The parent function to be: y = a * sin [k (x-d)] + c

    The period to be : pi radians

    The vertical translation, 'c' to be: 0

    The phase shift to be: pi/6, so d = pi/3

    However, when I used Desmos to graph the final function: y = 2 sin [2(x-pi/3)], I got the wrong answer. I used trial and error, and flipped it over the x-axis, and then I got the matching function. Why is it a -2 instead of a +2 then? Can anybody please explain this?


    Oh yeah, this is what sums up my past three hours trying this.
    I actually completed calculus I last semester and I am taking trig again over the summer.
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    Re: Determining a sinusoidal function from its graph, can amplitude be negative?

    I used Desmos to graph the final function: y = 2 sin [2(x-pi/3)], I got the wrong answer.
    try ...

    y = 2 sin [2(x+pi/6)]
    Thanks from Awesome31312
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    Re: Determining a sinusoidal function from its graph, can amplitude be negative?

    Quote Originally Posted by Awesome31312 View Post
    I have two questions. A lot of the sources I have read say that amplitude cannot be negative, because it is a distance, and we take the absolute value of distance. However, other sources say that A can be negative (like SymboLab). I actually completed calculus I last semester and I am taking trig again over the summer.
    That graph is stretched and shifted.
    $y=2\sin(x+\theta)$ so you need to determine $\theta$ the shifting factor.
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    Re: Determining a sinusoidal function from its graph, can amplitude be negative?

    Quote Originally Posted by skeeter View Post
    try ...

    y = 2 sin [2(x+pi/6)]
    Oh wow, that is interesting. The reason I did "pi/3" instead of "pi/6" is because when you multiply the quantity (x+pi/6) by 2 you end up with a constant (pi/3). Why did you choose "pi/6" to be the translation factor?



    Quote Originally Posted by Plato View Post
    That graph is stretched and shifted.
    $y=2\sin(x+\theta)$ so you need to determine $\theta$ the shifting factor.
    I know, and I found it to be "pi/6" but my answer is still incorrect.
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    Re: Determining a sinusoidal function from its graph, can amplitude be negative?

    Quote Originally Posted by Awesome31312 View Post
    Oh wow, that is interesting. The reason I did "pi/3" instead of "pi/6" is because when you multiply the quantity (x+pi/6) by 2 you end up with a constant (pi/3). Why did you choose "pi/6" to be the translation factor?
    first look at the graph ... it is a sine curve with period, $T = \pi$, shifted $\dfrac{\pi}{6}$ units left

    $y = A\sin[B(x+C)] + D$

    amplitude = $|A|$

    period = $T = \dfrac{2\pi}{|B|}$

    horizontal shift = $C$ ... $C < 0$, shift right ... $C > 0$ shift left

    vertical shift = $D$ ... $D < 0$ shift down ... $D > 0$ shift up
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    Re: Determining a sinusoidal function from its graph, can amplitude be negative?

    Quote Originally Posted by skeeter View Post
    first look at the graph ... it is a sine curve with period, $T = \pi$, shifted $\dfrac{\pi}{6}$ units left

    $y = A\sin[B(x+C)] + D$

    amplitude = $|A|$

    period = $T = \dfrac{2\pi}{|B|}$

    horizontal shift = $C$ ... $C < 0$, shift right ... $C > 0$ shift left

    vertical shift = $D$ ... $D < 0$ shift down ... $D > 0$ shift up
    Thank you, I understand it now.
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