Recent questions have dealt with calculations of various parts of a segment of a circle (chord, arc, sagitta, etc.). How, for example, can you find the arc length if you know the chord length and the height? The definitive explanation of these questions is found in a classic page from Ask Dr. Math, written by …
Here are a pair of problems related to the last of the three we looked at last time, involving inverse trigonometric function identities with subtle issues. They were probably intended to be rather simple problems (though going beyond what I typically see in American classes) by ignoring the subtleties, but if you approach them as …
Inverse Trig Problems With Unstated Restrictions Read More »
A couple recent questions involved errors made both by students and by the authors of their textbooks, involving trigonometric or inverse trigonometric functions. These offer some good lessons in pitfalls to be aware of.
In discussing the value of radians, we introduced the idea that trig functions are easier to evaluate that way. That raises the question, how do you find the value of a trigonometric function without a calculator, and how do calculators themselves do it? Let’s look into that.
A recent question reminded me that we hadn’t yet covered the topic of radians yet. We’ll look at several questions comparing radians to degrees, concluding with the recent question: Is a radian a unit, or something else?
Last month, four students from the same class wrote to us with the same question: Which is more accurate, the Law of Sines or the Law of Cosines? Those led to a couple deeper discussions, as we explored the context.
I am always interested in problems that can be solved in different ways, particularly because this can give a student a chance to be creative, as well as learning from experience that you don’t have to do it “the teacher’s way”. Here we’ll use trigonometry, and two different ways to add lines to a figure …
I’ve had several occasions in face-to-face tutoring lately to refer to a past post on mixing (that is, composition) of trig and inverse trig functions. Several recent questions have touched directly or indirectly on this same general idea and extended it, so I thought I’d post them.
(A new question of the week) Trigonometry identities can be hard to prove, and more so when they are specifically about a triangle.
Students sometimes wonder why the trigonometric functions (sine, cosine, tangent, secant, and so on) have the names they do, and how they relate to the corresponding terms in geometry. How are the tangent and secant functions related to tangent and secant lines in trigonometry? And what in the world is a sine? Here we’ll look …