Q 33 - Calculus

Question

Describe the graphs of the equations and provide alternative equations in the specified coordinate systems. 

Change $\theta =\frac{\mathrm{\pi }}{2}$ to the rectangular system 

Step-by-Step Solution

Answer

The rectangular coordinates is $x=0$

Step 1:Given information

The given expression is $\theta =\frac{\mathrm{\pi }}{2}$

Step 2:Simplification

The spherical coordinates$\theta =\frac{\mathrm{\pi }}{2}$ represents half of the $yz-$plane in $y\ge 0$

To convert to rectangular system, we use $\tan \theta =\frac{y}{x}$

$\Rightarrow \tan \left(\frac{\mathrm{\pi }}{2}\right)=\frac{y}{x}$

$\Rightarrow \frac{1}{0}=\frac{y}{x}$

$\Rightarrow x=o$

Tnerefore rectangular coordinates is  $x=0$