Given that the tangent to the curve makes a
positive angle with the positive direction of the -axis at the point
, determine the measure of the angle.
First, consider to be a function of and use implicit differentiation to determine for as follows. In the process of finding , keep in mind the Chain Rule.
Now, use the fact that to find as follows:
The measure of the positive angle that the tangent to the curve at the point makes with the positive part of the -axis is equal the inverse
tangent of the value of . In other words, it is equal to the inverse tangent of . Thus, the measure of the angle is .