This is a free lesson from our course in Trigonometry In this lesson, you'll learn the basics and explanation on how to convert rectangular coordinates to polar coordinates, and vice-versa. Rectangular coordinates and polar coordinates are two different ways of using two numbers to locate a point on a plane. Rectangular coordinates are in the form (x, y), where 'x' and 'y' are the horizontal and vertical distances from the origin. Polar coordinates are Polar coordinates are in the form: ( r , ), where 'r' is the distance from the origin to the point, and ' ' is the angle measured from the positive 'x' axis to the point. (More text below video...)
Other useful lessons:
 Name Polar Coordinates Convert Equation from Polar to Rectangular Form
(Continued from above) The rectangular coordinates can be converted to the polar coordinates by using the formulas
r = (x2 + y2) and = tan-1 (y/x),
For example, to convert (-3, 3) to polar coordinates, r = (x2 + y2) = ((-3)2 + 32) = 3 2 and = tan-1 (y/x) = tan-1 (3/(-3)) = - /4. So the polar coordinates in this case are (-3 2, - /4) or (3 2, 3 /4).
The polar coordinates can be converted to the rectangular coordinates by using the formulas
x = r cos and y = r sin .
For example, to convert the polar coordinates (4, /3) to rectangular coordinates, plug-in the values in the formulas x = r cos = 4 cos /3 = 2 and y = r sin = 4 sin /3 = 2 3. So the rectangular coordinate in this case is (2, 2 3). Once you go through the instructor's explanation in the video which brings in an element of real-class room experience and practice questions with solution, it'll be easy for you to understand and will help in problem solving.

Let us see one more example :
Convert the rectangular coordinates (1 , 1) to polar coordinates to three decimal places. Express the polar angle in degrees and radians.
You first find r using the formula
r = (x 2 + y 2) for the point (1 , 1).
r = (x 2 + y 2) = [1 + 1] = ( 2 )
You now find tan using the formula tan = y / x.
tan = 1 / 1
Using the tan-1 function, we obtain = / 4 or t = 45 Point (1 , 1) in rectangular coordinates may be written in polar for as follows :
( 2 , / 4 ) or ( 2 , 45 )

Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.
 - All of the Winpossible math tutorials have been designed by top-notch instructors and offer a comprehensive and rigorous math review of that topic. - We guarantee that any student who studies with Winpossible, will get a firm grasp of the associated problem-solving techniques. Each course has our instructors providing step-by-step solutions to a wide variety of problems, completely demystifying the problem-solving process! - Winpossible courses have been used by students for help with homework and by homeschoolers. - Several teachers use Winpossible courses at schools as a supplement for in-class instruction. They also use our course structure to develop course worksheets.

 Copyright © Winpossible, 2010 - 2011 Best viewed in 1024x768 & IE 5.0 or later version