Question

Find an equation for the plane y=5 in cylindrical coordinates. (Type theta for θ in your answer.)

a. r=5
b. z=5
c r=5sin(θ)
d. z=5cos(θ)

Answer 1

The equation for the plane y=5 in cylindrical coordinates is r=5sin(θ).

Step-by-step explanation:

The equation for the plane y=5 in cylindrical coordinates can be expressed as r=5sin(θ). In cylindrical coordinates, 'r' represents the distance from the origin to the point, and θ represents the angle from the positive x-axis to the point. So, a value of r=5sin(θ) would give us all the points on a circle with radius 5, centered at the origin, that lie in the plane y=5. The sin(θ) component ensures that the points lie in the upper half of the circle (y>0).