Question

What is the polar form of `(11,-8)`?

Answer 1

(`sqrt185`, 324)

Explanation:

Polar coordinates are expressed in the form (r, θ), where r is the distance from the origin to the point in question, and θ is the angle measured counterclockwise from the positive x-axis. From your question, I assume you have a handle on Cartesian coordinates.

Plot the point (11,-8) and then draw a line from the origin to that point. Use the Pythagorean Theorem to calculate the length of this line segment. The answer, `sqrt185`, is your r value.

Then, find θ using some basic trig (again, I'm assuming you have a good grasp of the primary trig ratios and how to use them in right triangles). From your drawing, you should see that the angle clockwise from the positive x-axis to your line segment is equal to `tan^-1` (8/11) or approximately 36 degrees. In order to find the angle counterclockwise from the positive x-axis (as mathematicians virtually always do), subtract 36 from 360. The difference, 324, is your value for θ. Hence the polar coordinates you're looking for are (`sqrt185`, 324).