Angle between function and axis

[fermio]

Homework Statement

What angle is between function $$y=\sqrt{3}x$$ and Ox axis?

Homework Equations

For example is logicaly clear that angle between function y=x is 45 degrees or $$\frac{\pi}{4}$$

The Attempt at a Solution

I just know that answer is $$\frac{\pi}{3}$$, but can't understand how to get it.

 

[CompuChip]

Hint: the angle between the function and the x-axis is the same angle as between the tangent line at x = 0 and the x-axis (draw a picture to see why).
Can you solve it now?

 

[fermio]

If x=0 then y=0. I can't understand. More concretly, how to calculate it?

 

[Defennder]

Why do you need to set x,y=0? The question is why the angle between the line graph and the axis is pi/3, not the angle between the point (0,0) and the x-axis, which doesn't make sense. You can see that the graph is a line right? Now, let theta be the angle between the line and the x-axis. Do you know of way to find theta using trigo? You'll have to draw a triangle to see it.

 

[HallsofIvy]

The slope of a line, such as y= x, is than tangent of the angle between the line and the x-axis. As you said before, the angle between the line y= x and the x-axis is $\pi/4$. tan($\pi/4$)= 1. What is the slope of y= $\sqrt{3}$ x? What angle has that tangent?

 

[fermio]

$$\arctan\sqrt{3}=\frac{\pi}{3}$$

 

[CompuChip]

Why do you need to set x,y=0? The question is why the angle between the line graph and the axis is pi/3, not the angle between the point (0,0) and the x-axis, which doesn't make sense.

Sorry, I misread the question, I thought it said $$y = \sqrt{3x} = (3x)^{1/2}$$ instead of $$y = \sqrt{3}x = (3)^{1/2} \cdot x$$. I had a picture in my mind of drawing the tangent line at the origin and then calculating the angle of that with the x-axis, which could of course be done at any point. But since the function is just a straight line, it doesn't matter in this case (y' does not depend on x)

 

[fermio]

$$\tan\alpha=\frac{y}{x}=\frac{x\sqrt{3}}{x}=\sqrt{3}$$
$$\alpha=\arctan \sqrt{3}=\frac{\pi}{3}$$

 

[CompuChip]

Yep, that's the way to get it.