Find x-intercepts & Intervals

[harpazo]

Is there a way to find the x-intercepts and the intervals where a given trig function is increasing WITHOUT graphing?

For example, find the x-intercepts and indicate the intervals where y = - 2 sin (2x) is increasing WITHOUT graphing. Is this possible?

 

[pka]

I assume that this is not calculus.
First \(\sin(\theta)=0\) if \(\theta=\pi\cdot n\) where \(n\in\mathbb{Z}\)
So in order for \(2x=\pi\cdot n\) then \(x=\dfrac{\pi}{2}\cdot n\)

The \(\sin(\theta)\) is increasing for \(\theta \in \left(\frac{-\pi}{2},\frac{\pi}{2}\right)\). Then what happens?
You finish and post.

 

[harpazo]

I assume that this is not calculus.
First \(\sin(\theta)=0\) if \(\theta=\pi\cdot n\) where \(n\in\mathbb{Z}\)
So in order for \(2x=\pi\cdot n\) then \(x=\dfrac{\pi}{2}\cdot n\)

The \(\sin(\theta)\) is increasing for \(\theta \in \left(\frac{-\pi}{2},\frac{\pi}{2}\right)\). Then what happens?
You finish and post.

Then what happens?

 

[pka]

Then what happens?

That is what we asked you. Are you now asking us to do your work for you?
I will tell you that if \(\sin(x)\) is increasing on \((a,b)\) then it is also increasing on \((a+\pi,b+\pi)\)
So please answer the question!

 

[harpazo]

That is what we asked you. Are you now asking us to do your work for you?
I will tell you that if \(\sin(x)\) is increasing on \((a,b)\) then it is also increasing on \((a+\pi,b+\pi)\)
So please answer the question!

For y = sin x, the function is increasing on the open interval (-pi/2, pi/2). The period of this trig function is 2pi. So, the function is increasing on (-pi/2 + 2pi•n, pi/2 + 2i•n), where n is any integer.

 

[MarkFL]

For y = sin x, the function is increasing on the open interval (-pi/2, pi/2). The period of this trig function is 2pi. So, the function is increasing on (-pi/2 + 2pi•n, pi/2 + 2i•n), where n is any integer.

Yes, check out this graph to see some intervals where \(y=\sin(x)\) is increasing. Move the slider...

Desmos | Graphing Calculator

www.desmos.com

 

[harpazo]

Yes, check out this graph to see some intervals where \(y=\sin(x)\) is increasing. Move the slider...

Desmos | Graphing Calculator

www.desmos.com

Cool.