Section 3.6

Problem 1

The domain of the mathematical arctan function is . This is because we think of arctan(x) as the inverse of the "branch" of tan(x) passing through the origin. However, in many practical situations, the value of tan(x) is actually obtained from the xy-coordinates of a point on a ray making an angle with the x-axis, and one would like to use the arctan(x) function to determine the unique angle in the interval that the ray makes with the positive x-axis. Using information from the coordinates, as well as the arctan(x) function, this is possible.

  1. Determine the angle between the positive x-axis, and the ray starting at the origin and passing through the point (-4,3). Do the same thing for the rays through the points (1,2), (-5,-7) and (2, -5).

  2. Describe in general how to use the mathematical function arctan(x) to find the angle a ray through (x,y) makes with the positive x-axis.

Aside:In computer languages like PERL and C, the arctan function is actually implemented in the way suggested by this problem. Namely, atan(x,y) returns the angle that the ray passing through (x,y) makes with the positive x-axis.

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    OU Math Study Group, Copyright 1995.
    Last modified: Fri Nov 10 11:42:39 CST 1995