#### harpazo

##### Full Member

- Joined
- Jan 31, 2013

- Messages
- 783

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

- Thread starter harpazo
- Start date

- Joined
- Jan 31, 2013

- Messages
- 783

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

- Joined
- Jan 29, 2005

- Messages
- 9,809

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.

- Joined
- Jan 31, 2013

- Messages
- 783

Then what happens?

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.

- Joined
- Jan 29, 2005

- Messages
- 9,809

That is what we asked you. Are you now asking us to do your work for you?Then what happens?

I will tell you that if \(\sin(x)\) is increasing on \((a,b)\) then it is also increasing on \((a+\pi,b+\pi)\)

- Joined
- Jan 31, 2013

- Messages
- 783

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.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!

- Joined
- Nov 24, 2012

- Messages
- 2,930

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

www.desmos.com

- Joined
- Jan 31, 2013

- Messages
- 783

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

## Desmos | Graphing Calculator

www.desmos.com