Find x-intercepts & Intervals

harpazo

Full Member
Joined
Jan 31, 2013
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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?
 
I assume that this is not calculus.
First sin(θ)=0\sin(\theta)=0 if θ=πn\theta=\pi\cdot n where nZn\in\mathbb{Z}
So in order for 2x=πn2x=\pi\cdot n then x=π2nx=\dfrac{\pi}{2}\cdot n

The sin(θ)\sin(\theta) is increasing for θ(π2,π2)\theta \in \left(\frac{-\pi}{2},\frac{\pi}{2}\right). Then what happens?
You finish and post.
 
I assume that this is not calculus.
First sin(θ)=0\sin(\theta)=0 if θ=πn\theta=\pi\cdot n where nZn\in\mathbb{Z}
So in order for 2x=πn2x=\pi\cdot n then x=π2nx=\dfrac{\pi}{2}\cdot n

The sin(θ)\sin(\theta) is increasing for θ(π2,π2)\theta \in \left(\frac{-\pi}{2},\frac{\pi}{2}\right). Then what happens?
You finish and post.

Then what happens?
 
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)\sin(x) is increasing on (a,b)(a,b) then it is also increasing on (a+π,b+π)(a+\pi,b+\pi)
So please answer the question!
 
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)\sin(x) is increasing on (a,b)(a,b) then it is also increasing on (a+π,b+π)(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.
 
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)y=\sin(x) is increasing. Move the slider...

 
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