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Thread: How do you know where a sine function is increasing or decreasing?

  1. #1
    s3a
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    How do you know where a sine function is increasing or decreasing?

    How do you know where a sine function is increasing or decreasing?
    Thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by s3a View Post
    How do you know where a sine function is increasing or decreasing?
    Thanks!
    If $\displaystyle f\!\left(x\right)=\sin x$, then $\displaystyle f\!\left(x\right)$ is increasing when $\displaystyle f^{\prime}\!\left(x\right)>0$ and it is decreasing when $\displaystyle f^{\prime}\!\left(x\right)<0$.
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  3. #3
    s3a
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    Quote Originally Posted by Chris L T521 View Post
    If $\displaystyle f\!\left(x\right)=\sin x$, then $\displaystyle f\!\left(x\right)$ is increasing when $\displaystyle f^{\prime}\!\left(x\right)>0$ and it is decreasing when $\displaystyle f^{\prime}\!\left(x\right)<0$.
    Actually what I am trying to ask is over which intervals is the function positive or negative? And I don't think what you said is true because the wave ALSO decreases when f(x)>/=0, and the wave ALSO increases when f(x)</=0.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by s3a View Post
    Actually what I am trying to ask is over which intervals is the function positive or negative? And I don't think what you said is true because the wave ALSO decreases when f(x)>/=0, and the wave ALSO increases when f(x)</=0.
    But note that $\displaystyle f^{\prime}\!\left(x\right)>0$ doesn't necessarily mean that $\displaystyle f\!\left(x\right)>0$ and that $\displaystyle f^{\prime}\!\left(x\right)<0$ doesn't necessarily mean that $\displaystyle f\!\left(x\right)<0$ In the case of $\displaystyle f^{\prime}\!\left(x\right)=\cos x$, there will be two intervals where $\displaystyle f^{\prime}\!\left(x\right)<0$ but $\displaystyle f\!\left(x\right)>0$ and $\displaystyle f^{\prime}\!\left(x\right)>0$ but $\displaystyle f\!\left(x\right)<0$

    So what intervals is $\displaystyle \cos x<0$ and $\displaystyle \cos x>0$?
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  5. #5
    s3a
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    I think I found it in my teacher's notes (just wasn't looking in the right place). But, I just need confirmation:

    Is the following true or false?:

    Intervals of Increase:
    [Xmin, Xmin + period/2]

    Intervals of Decrease:
    [Xmax, Xmax + period/2]
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  6. #6
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    Why don't you tell us what question you are REALLY asking? You originally asked "How do you know where a sine function is increasing or decreasing?" and that was interpreted as a function that involves sine in some way. Are you asking specifically about sin(x)? Or about $\displaystyle sin(\omega(x+ \Omega))$?
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