Answer:
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
The equation of the plane y=4x in cylindrical coordinates is, [tex]sin\theta-4cos\theta=0[/tex]
To find the equation of plane in cylindrical coordinates,
We have to substitute ,
[tex]x=rcos\theta\\\\y=rsin\theta\\\\z=z[/tex]
Given equation of plane is, [tex]y=4x[/tex]
Substitute values in equation of plane.
[tex]rsin\theta=4(rcos\theta)\\\\sin\theta=4cos\theta\\\\sin\theta-4cos\theta=0[/tex]
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