Question

Convert the polar equation into a rectangular equationθ= π/4

Answer 1

First, we must remember the following set of relations:

$\begin{gathered} \cos\theta=\frac{x}{r} \\ \sin\theta=\frac{y}{r} \\ \tan\theta=\frac{y}{x} \\ x^2+y^2=r^2 \end{gathered}$

Then we have:

$\begin{gathered} \theta=\frac{\pi}{4} \\ \tan\frac{\pi}{4}=\frac{y}{x}=1 \\ \frac{y}{x}=1 \\ \therefore y=x \end{gathered}$