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

Short answer

The rectangular coordinates is$x=0$

Step-by-step solution

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 $x=0$