MDME: MANUFACTURING, DESIGN, MECHANICAL ENGINEERING 

POLAR COORDINATES


You can use Polar coordinates or Rectangular (Cartesian) coordinates to define points on the plane.

You can use polar coordinates and Cartesian (x, y) coordinates (also known as rectangular coordinates) at any time to describe the same location on the coordinate plane.

Either one is better for cerain situations, so it’s important to know how to change between the two.

  • Cartesian coordinates are best for graphs of straight lines or simple curves.
  • Polar coordinates are better for complex graphs that you can’t plot with Cartesian coordinates.

When changing to and from polar coordinates, it is often easier if angle is in radians, not degrees. You can make the change by using the conversion factor

180o = Π radians

If not using radians, make sure your calculator is in the right mode (Degrees).

In above diagram, a point could be given in (x, y) or (r, Θ) coordinates.

What is the relationship between them?

From the basic trigonometric definitions,

So, to find (x,y) from the polar coordinates (r, Θ), we use;

To find (r, Θ) from the rectangular coordinates (x, y) we use;

To get the radius...

r = √(x2 + y2)

and to get the angle...

Be careful though. The angle may not be in the correct quadrant! You need to draw the point to see which quadrant it is in, then give it the correct angle. The calculator cannot do this because it divides the (y/x) first before it finds the inverse tangent. So it thinks a quadrant 3 angle is in quadrant 1, and a quadrant 4 angle is in quadrant 2.

  • Quadrant 1: Θ
  • Quadrant 2: 180 - Θ
  • Quadrant 3: 180 + Θ
  • Quadrant 4: 360 - Θ



Questions:

Homework Assignment: 

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