Chapter 13: Q 69. (page 1068)

Let $a$ be a constant. Prove that the equation of the plane $x = a$ is $r = a s e c θ$ in cylindrical coordinates.

Short Answer

Expert verified

Use the transformation $x = r \cos θ, y = r \sin θ, z = z$ to prove the mentioned relation.

Step by step solution

Given Information

Equation of plane in rectangular coordinates is given as $x = a$ ( $a$ is constant).

Simplification

$x = r \cos θ, y = r \sin θ, z = z$ are cylindrical coordinates.

Use $x = r \cos θ$ in the given equation to convert equation to cylindrical coordinates.

$x = a$

$\Rightarrow r \cos θ = a$

$r = \frac{a}{\cos θ}$

$r = a \sec θ$

Hence proved.

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Let $a$ be a constant. Prove that the equation of the plane $x = a$ is $r = a s e c θ$ in cylindrical coordinates.

Short Answer

Step by step solution

Given Information

Simplification

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Let abe a constant. Prove that the equation of the planex=a isr=asecθin cylindrical coordinates.

Short Answer

Step by step solution

Given Information

Simplification

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Let $a$ be a constant. Prove that the equation of the plane $x = a$ is $r = a s e c θ$ in cylindrical coordinates.