Two distances are required to specify the location of a point relative to an origin in two...

Two distances are required to specify the location of a point relative to an origin in two-dimensional space (Fig. P3.6):

• The horizontal and vertical distances (x, y) in Cartesian coordinates.

• The radius and angle (r, θ) in polar coordinates.

It is relatively straightforward to compute Cartesian coordi­nates (x, y) on the basis of polar coordinates (r, θ). The reverse process is not so simple. The radius can be computed by the following formula:

If the coordinates lie within the first and fourth coordinates (i.e., x > 0), then a simple formula can be used to compute θ:

FIGURE P3.6

The difficulty arises for the other cases. The following table summarizes the possibilities:

Write a well-structured M-file to calculate r and θ as a func­tion of x and y. Express the final results for θ in degrees. Test your program by evaluating the following cases: