Which Surface Does X=cos(t), Y=sin(t), Z=t Lie On?

[weckod]

i have the parametric equations to the curve X = cos t y = sin t and z = t

which of the following surfaces does it lie on?

1)circular cylinder
2)elliptic paraboloid
3)sphere
4)plane

I think there's more than one answer but i can't seem to picture it from the equation on why. Anyone know y?

 

[Cyrus]

The x-y traces are circles. X^2+y^2 = cos(t)^2 + sin(t)^2 =1
Z=t, which means the height increases with the variable t.

Its going to lie on a circular cylinder, but it will be in the shape of a HELIX, wrapped around that cylinder of course.

 

[weckod]

The x-y traces are circles. X^2+y^2 = cos(t)^2 + sin(t)^2 =1
Z=t, which means the height increases with the variable t.

Its going to lie on a circular cylinder, but it will be in the shape of a HELIX, wrapped around that cylinder of course.

Hey thanks for the answer but how could u just take an x^2 + y^2 = cos(t)^2 + sin(t)^2 = 1 just like that??

im lookin athe parametrics and i see no sqs... how could u know its sqs and not like x^3 or something??

 

[Cyrus]

practice. You will easily recognize tricks like that too with time. X^3 would do you no good, because its not a trig identity; however, the x,y^2s do allow u to use a trig identity.