# Find x-intercepts & Intervals

#### harpazo

##### Full Member
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
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
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
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 $$(a+\pi,b+\pi)$$

#### harpazo

##### Full Member
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 $$(a+\pi,b+\pi)$$
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
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...

#### harpazo

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

Cool.