I'm self-studying from Vector Analysis and Cartesian Tensors by Kendall because my lecturer is somewhat lacking, and I got conceptually stuck on excersise 1.11 dealing with direction cosines. What does it mean when we say that a line makes an obtuse angle with an axis? Is there a norm on which direction you're supposed to be looking from?
Also, a cosine squared appears in here (which gives 4 candidate solutions), but even if I reject two because it's obtuse or acute, that still leaves me with two potential answers and the solutions only say 135 degrees.