# Consider the polar equation \theta = \frac{7}{4}\pi What is the equation in Cartesian...

## Question:

Consider the polar equation {eq}\theta = \frac{7}{4}\pi {/eq}

What is the equation in Cartesian (rectangular) coordinates equivalent to this polar equation?

## Converting Between Polar and Cartesian:

A polar equation can be converted to a Cartesian equation (or a Cartesian equation can be converted to a polar equation) by making use of these trigonometric facts:

1) {eq}x^{2}+y^{2}=r^{2} {/eq}

2) {eq}x=r\cos\theta {/eq} and {eq}y=r\sin\theta {/eq}

3) {eq}\theta =\tan^{-1}\left ( \frac{y}{x} \right ) {/eq}

Substitution will be necessary to change {eq}r's {/eq} and {eq}\theta's {/eq} to {eq}x's {/eq} and {eq}y's {/eq} (or vice versa).