Hey everyone!
I have a calculus exam coming up (tomorrow, actually) and I'm having trouble figuring out a practice question. I was hoping somebody here could lend a hand
Please and Thank You!
So the question has to do with sketching a curve/surface.
Sketch;
x=cos(4t), y=sin(4t), z=1----------------------------------------------------------------------------------
Now there was a previous question that was similar to the above. The info given was x=2tcos(t), y=3tsin(t), z=t^2
It ended up being a paraboloid, centered on the z-axis, with a swirling curve inside its boundaries.
It was solved by using the identity
sin^2x + cos^2x = 1which ended up giving
(x/2)^2 + (y/3)^2 = t^2 = zand in turn,
(x^2)/4 + (y^2)/9 = z (the corresponding paraboloid function)
From there, it was determined that z increases, while x and y increase/decrease periodically, creating the swirl.
So when I try a similar method of solving the (initial) question, I can't seem to formulate a surface equation.
I guess I'd like somebody to help me solve this or push me in the right direction.
Thanks DTF!