Q 33. - Calculus

Question

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.

$\theta =\frac{\mathrm{\pi }}{4}$

Step-by-Step Solution

Answer

The required equation is $y=x$.

Step 1. Given information.

The given equation in polar coordinates is:

$\theta =\frac{\mathrm{\pi }}{4}$

Step 2. Find the equation in rectangular coordinates.

Use the formula $\tan \theta =\frac{y}{x}$,

$$\begin{gathered} \tan \frac{\mathrm{\pi }}{4}=\frac{y}{x} \\ 1=\frac{y}{x} \left[\mathrm{Since} \tan \frac{\mathrm{\pi }}{4}=1\right] \\ y=x \end{gathered}$$

Therefore, the equation in rectangular coordinates is $y=x$.