Representing a curve with a vector valued function

[dietcookie]

Homework Statement

See attached image

Homework Equations

The Attempt at a Solution

Why use x=2sint??

Would it be incorrect to use the x=2cost (versus the given x=2sint)? My professor instructed us to not use the given parameters in the book and to come up with our own, and I would of used x=2cost which would of changed the resulting vector-valued function (Resulting in r = 2Cos(t)i+2Sin(t)j+4Cos²tk)

Thanks.

 

[Dick]

Either one is fine. The difference between the two is also the same thing as changing the parameter t into pi/2-t. Do you see why?

 

[dietcookie]

I understand the identity sin(t)=cos[(pi/2)-t], but I really don't see why using either parameters x=2sint or x=2cost is equivalent. The book wants me to use x=2sint, wouldn't the equivalent then be actually x=2cos([(pi/2)-t]) ? Thanks

 

[Dick]

I understand the identity sin(t)=cos[(pi/2)-t], but I really don't see why using either parameters x=2sint or x=2cost is equivalent. The book wants me to use x=2sint, wouldn't the equivalent then be actually x=2cos([(pi/2)-t]) ? Thanks

If r(t) is a curve then r(a-t) represents the same curve. It goes through the same points, just at different values of t.