multivariable: exam review: parametric equations of surface of revolution?

[3MoreYearsAtUF]

Not really sure how to begin this problem, any help would be appreciated

Determine the parametric equations of the surface of revolution obtained by rotating the curve in the xy-plane given by y=sinx for 0<=x<=pi about the x-axis using x and the angle theta through which the curve has been turned as parameters.

answer: x=x, y=sin(x)cos(theta), z=sin(x)sin(theta), 0<=theta<=2(pi)

 

[3MoreYearsAtUF]

any help is appreciated

 

[tkhunny]

Your task is somewhat simplified if you take a stroll down the x-axis in the positive direction. Careful! It's pretty narrow. You don't want to fall off.
Also, I probably should mention that the y-axis is the horizontal axis when you loo back toward the y-z plane. This will be important, later.

When you get past x = pi, stop, turn around, and take a look at it. What do you see? The point, here is that you should be able to imagine the circular cross section from this point of view.

Your task, now, is to imagine the radius of each cross section. You can find this by taking your stroll toward the Origin, inside the figure, and picking a spot.

At x = pi, the radius is zero.
At x = 2pi/3, the radius is...hey, wait a minute, the radius is just sin(x) for every x in the Domain. You must see this in order to continue.

Your final task is to write equations for circles of varius radii in the y-z plane. You've seen that, I expect. y = Radius*cos(theta) and z = Radius*sin(theta)

See, you just had to take a little walk and clear your head!