1. The term "polar coordinate system" was first used by Gregorio Fontana and was translated into English by George Peacock in 1816.
2. Polar coordinates can be converted to Cartesian coordinates using the equations x = rcos(θ) and y = rsin(θ).
3. Different types of curves, such as circles, ellipses, parabolas, hyperbolas, and rose curves can be expressed in polar coordinates.
The article is generally reliable and trustworthy. It provides a comprehensive overview of polar coordinates and their applications in mathematics. The sources cited are credible and the information provided is accurate. The article does not appear to have any biases or one-sided reporting; it presents both sides of the argument equally. Furthermore, all claims made are supported with evidence from credible sources.
The only potential issue with the article is that it does not explore counterarguments or present any risks associated with using polar coordinates. However, this is likely due to the fact that there are no known risks associated with using polar coordinates, so this omission does not detract from the overall reliability of the article.