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Math Help - sin(x), sin(2x), sin(1/2)....what is the period?

  1. #1
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    sin(x), sin(2x), sin(1/2)....what is the period?

    sin(x), sin(2x), sin(1/2)....what are the periods?

    Pls explain to me the concepts involved so I can remember more clearly.

    Thanks.
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  2. #2
    Senior Member Educated's Avatar
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    A period is how long it takes for the wave to complete one full cycle.

    Sin(x) has a period of 2 \pi in radians, or 360^{\circ} in degrees. This means that if you draw the graph of sin(x), the graph would take 2 \pi or 360^{\circ} to complete one full cycle. Which is a period.

    Sin(2x) has a period of half of sin(x)
    Sin(0.5x) has a period of double of sin(x)

    The 2 in front of the x doubles the speed of one wave, which means that it halves the time, and since a period is the length of time for one full cycle, the period is halved as well. Vise versa for the 0.5.

    Just think of it as this way:

    sin(x) = \text{Normal period}

    sin(2x) = \frac{\text{Normal period}}{2}

    sin(0.5x) = \frac{\text{Normal period}}{0.5}
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  3. #3
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    Quote Originally Posted by stupidguy View Post
    sin(x), sin(2x), sin(1/2)....what are the periods?

    Pls explain to me the concepts involved so I can remember more clearly.

    Thanks.
    \displaystyle\ Sin(0)=0, \; \; Sin\left(\frac{{\pi}}{2}\right)=1, \; \; Sin({\pi})=0,\; \; Sin\left(\frac{3{\pi}}{2}\right)=-1,\; \; Sin(2{\pi})=0

    Sinx goes through a full period in 2{\pi} radians.

    Finding 3 consecutive zeros will discover the period, as the centreline of the graph is the x-axis.
    Simplest is to start at zero.

    \displaystyle\ Sin(2x)=0 for \displaystyle\ x=0 and \displaystyle\ 2x={\pi}\Rightarrow\ x=\frac{{\pi}}{2} and 2x=2{\pi}\Rightarrow\ x={\pi}

    therefore Sin(2x) has period {\pi} radians.

    \displaystyle\ Sin\left(\frac{x}{2}\right)=0\Rightarrow\ x=0, \;\; x=2{\pi}, \;\; x=4{\pi}

    so the period of \displaystyle\ Sin\left(\frac{x}{2}\right) is 4{\pi} radians.


    Alternatively......

    SinA=Sin(A+2{\pi})

    Sinx=Sin(x+2{\pi}) has a period of 2{\pi} radians

    Sin(2x)=Sin(2x+2{\pi})=Sin[2(x+{\pi})] which therefore has a period of {\pi} radians

    \displaystyle\ Sin\left(\frac{x}{2}\right)=Sin\left(\frac{x}{2}+2  {\pi}\right)=Sin\left[\frac{1}{2}(x+4{\pi})\right] has a period of 4{\pi} radians
    Last edited by Archie Meade; September 6th 2010 at 06:03 AM. Reason: added alternative
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  4. #4
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    Quote Originally Posted by Educated View Post
    A period is how long it takes for the wave to complete one full cycle.

    Sin(x) has a period of 2 \pi in radians, or 360^{\circ} in degrees. This means that if you draw the graph of sin(x), the graph would take 2 \pi or 360^{\circ} to complete one full cycle. Which is a period.

    Sin(2x) has a period of half of sin(x)
    Sin(0.5x) has a period of double of sin(x)

    The 2 in front of the x doubles the speed of one wave, which means that it halves the time, and since a period is the length of time for one full cycle, the period is halved as well. Vise versa for the 0.5.

    Just think of it as this way:

    sin(x) = \text{Normal period}

    sin(2x) = \frac{\text{Normal period}}{2}

    sin(0.5x) = \frac{\text{Normal period}}{0.5}
    You are talking in the context of physics becos u use terms like speed and wave. LOL
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  5. #5
    Senior Member yeKciM's Avatar
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    just to add that if you have shifted signal (  \sin {x \pm A}), left or right it will have same period but just moved to one or another side or if you multiply signal for example that "sin" (  A\sin {x}) it will again have same period but just amplitude bigger or smaller depending by which number is multiplying (if it is more or less than 1)... same thing when looking at those signals of yours if it's variable (in this case "x") is multiplied with number bigger than 1 that means that it will change that many times faster than usual, and if is multiplied with number less than 1 it will go that many times slower than normal
    Attached Thumbnails Attached Thumbnails sin(x), sin(2x), sin(1/2)....what is the period?-sinus.jpg  
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