Here’s a straightforward application of arctangent that, a generation ago, used to be taught in a typical Precalculus class (or, as it was called back then, analytical geometry).
Find the smallest angle between the lines and .
This problem is almost equivalent to finding the angle between the vectors and . I use the caveat almost because the angle between two vectors could be between and , while the smallest angle between two lines must lie between and .
This smallest angle can be found using the formula
,
where and are the slopes of the two lines. In the present case,
.
Not surprisingly, we obtain the same answer that we obtained a couple of posts ago using arccosine. The following picture makes clear why .
In tomorrow’s post, I’ll explain why the above formula actually works.
I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
View all posts by John Quintanilla
and
.
In tomorrow’s post, I’ll explain why the above formula actually works.
Mean Green Math 