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

1. ## 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!

2. Originally Posted by s3a
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 $\displaystyle f^{\prime}\!\left(x\right)<0$.

3. Originally Posted by Chris L T521
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.

4. Originally Posted by s3a
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 $\displaystyle \cos x>0$?

5. 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]

6. 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 $\displaystyle sin(\omega(x+ \Omega))$?