Copyright

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).

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given {eq}\theta = \frac{7}{4}\pi {/eq}, we can replace {eq}\theta {/eq} with {eq}\tan^{-1}\left ( \frac{y}{x} \right ) {/eq}

{eq}\tan^{-1}\l...

See full answer below.


Learn more about this topic:

Loading...
Graphing Functions in Polar Coordinates: Process & Examples

from

Chapter 24 / Lesson 1
4.9K

Learn how to graph polar equations and plot polar coordinates. See examples of graphing polar equations. Transform polar to rectangular coordinates and vice versa.


Related to this Question

Explore our homework questions and answers library