Graph r(t) = <t^2, cos t, sin t>

[crazynut52]

r(t)= <t^2, cost, sint>

Does anyone have a graphing program to make a picture of this, thanks.

 

[graphic7]

r(t)= <t^2, cost, sint>

Does anyone have a graphing program to make a picture of this, thanks.

What kind of range are you looking for?

I assume this is a vector field?

 

[crazynut52]

its a curve of that function. I'm not sure on the range, I guess just enough to show the pattern. I believe it is a cos sin circle coming out the x axis.

 

[graphic7]

Try this:

http://graphical.shacknet.nu/image1.jpg

 

[quantumdude]

The implied range is that x>0, and that y and z must both be between -1 and 1 (inclusive). I don't have a graphing utility handy, but what I would do is find the 2D curve in each coordinate plane by eliminating the parameter. So, in the xy plane, you have y(x)=arccos(x^1/2), in the xz plane you have z(x)=arcsin(x^1/2), and in the yz plane you have y²+z²=1.

Basically, the curve is constrained to the unit cylinder y²+z²=1, and as it goes around it moves forward on the x-axis, starting from x=0.

 

[graphic7]

The implied range is that x>0, and that y and z must both be between -1 and 1 (inclusive). I don't have a graphing utility handy, but what I would do is find the 2D curve in each coordinate plane by eliminating the parameter. So, in the xy plane, you have y(x)=arccos(x^1/2), in the xz plane you have z(x)=arcsin(x^1/2), and in the yz plane you have y²+z²=1.

Basically, the curve is constrained to the unit cylinder y²+z²=1, and as it goes around it moves forward on the x-axis, starting from x=0.

My plot seems to agree.

 

[graphic7]

If you need a larger range, just request it.

 

[quantumdude]

If you need a larger range, just request it.

There is no larger range. The implied range that I stated is the maximal range.

 

[graphic7]

There is no larger range. The implied range that I stated is the maximal range.

Only in the y and z directions, though. I just replotted from 0 to 1000 and you really get to see the unit cyclinder take form.

 

[quantumdude]

Only in the y and z directions, though. I just replotted from -1000 to 1000 and you really get to see the unit cyclinder take form.

Ah, I see what you're saying. You mean a larger range in your picture. What I was saying is that the range implied by the equations is the maximal range, and that if there is any modification to that range in the problem, it can only be smaller, not bigger.

 

[graphic7]

Ah, I see what you're saying. You mean a larger range in your picture. What I was saying is that the range implied by the equations is the maximal range, and that if there is any modification to that range in the problem, it can only be smaller, not bigger.

Ah, sorry for the confusion.