Find x-intercepts & Intervals

harpazo

Full Member
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Jan 31, 2013
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783
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

Elite Member
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Jan 29, 2005
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9,809
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

Full Member
Joined
Jan 31, 2013
Messages
783
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

Elite Member
Joined
Jan 29, 2005
Messages
9,809
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

Full Member
Joined
Jan 31, 2013
Messages
783
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

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
2,930
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...

 
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