Q 48. - Calculus

Question

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$x=0$

Step-by-Step Solution

Answer

The required equation is $\theta =\frac{\mathrm{\pi }}{2}$.

Step 1. Given information.

The given equation in rectangular coordinates is:

$x=0$

Step 2. Find the equation in rectangular coordinates.

$x=0$

As we know that $x=r \cos \theta$ in polar coordinates, then substitute the value of x,

$$\begin{gathered} r \cos \theta =0 \\ \cos \theta =\frac{0}{r} \\ \cos \theta =0 \\ \theta =\frac{\mathrm{\pi }}{2} \left[\cos \frac{\mathrm{\pi }}{2}=0\right] \end{gathered}$$

Therefore, the equation in polar coordinates is $\theta =\frac{\mathrm{\pi }}{2}$.