Final answer:
To convert an equation from spherical to rectangular coordinates (φ = 6, z ≥ 0), we use the transformation formulas. The resulting equation for the given plane in rectangular coordinates is x cos(6) + y sin(6) = 0.
Step-by-step explanation:
The student is asking to find the equation in rectangular coordinates for an equation given in spherical coordinates where φ = 6 and z ≥ 0. The equation in spherical coordinates can be expressed using spherical to rectangular coordinate transformation formulas. In the context of the question, φ represents the azimuthal angle and is usually denoted by Φ in spherical coordinates. The relationship between the coordinates is given by:
x = r sin(θ) cos(φ)
y = r sin(θ) sin(φ)
z = r cos(θ)
Since φ = 6 is constant and z ≥ 0, we are dealing with a plane in three-dimensional space that is rotated about the z-axis by an angle of 6 radians. The equation for this plane in rectangular coordinates does not depend on 'r' since 'r' can be any positive real number due to z ≥ 0 condition.
Instead, x and y are derived from the above relationships and the equation of the plane is simply x cos(6) + y sin(6) = 0.