Question

Find an equation for the plane y=4x in cylindrical coordinates. (Type theta for θ in your answer.)

Answer 1

Answer:

sinθ - 4cosθ = 0

Step-by-step explanation:

Given the equation of a plane in rectangular coordinates to be y = 4x.

The cylindrical coordinates of the axis is as given below;

x = rcosθ

y = rsinθ

z = z

Since there is no z coordinate in the equation of the plane given, we will only substitute x = rcosθ and y = rsinθ into the equation y = 4x and simply the result as shown;

y = 4x

rsinθ = 4( rcosθ)

rsinθ = 4rcosθ

sinθ = 4cosθ

sinθ - 4cosθ = 0

Hence the equation for the plane in cylindrical coordinate is expressed as sinθ - 4cosθ = 0