Find the equation for the surface formed by rotating (x = 3*cos(y)) about the y axis.
Your answer must not contain radical symbols (square root signs).
To find the equation for the surface formed by rotating (x = 3*cos(y)) about the y-axis, we can use the concept of parametric equations.
Let's consider a point on the graph, which we'll call P, with coordinates (x, y). When we rotate this point around the y-axis, it sweeps out a circle. The x-coordinate of the point on the resulting surface is the same as the x-coordinate of P (x), and the y-coordinate of the point on the resulting surface is the same as the z-coordinate of P (z).
To express the equation in terms of x, y, and z, we need to eliminate y. We can do that by rearranging the given expression:
x = 3*cos(y)
Now, let's replace x with r*cos(theta) and z with r*sin(theta) to represent the point P in polar coordinates:
r*cos(theta) = 3*cos(y)
r*sin(theta) = y
Next, we can eliminate y by substituting r*sin(theta) in place of y:
r*cos(theta) = 3*cos(r*sin(theta))
This is the equation for the surface formed by rotating (x = 3*cos(y)) about the y-axis. It is expressed in polar coordinates (r, theta). Note that this equation cannot be simplified further without using radical symbols, as the cosine function is involved.
In conclusion, the equation for the surface formed by rotating (x = 3*cos(y)) about the y-axis is:
r*cos(theta) = 3*cos(r*sin(theta))