A question in this month’s Mathematics Teacher asks about the range of \(\sin(\sin(x))\). My initial concern about this was over the units of the input and output of the sine function. I’ll summarize those briefly, but this post is about the resolution of those concerns by clarifying what a “degree” is in the first place….
Month: April 2016
Every Third Triangular Number
This is a quick proof based on an observation inspired by “Mathematical Lens” in the May 2016 Mathematics Teacher (“Fence Posts and Rails” by Roger Turton). A triangular number is the sum of all integers from 1 to n. The general formula for T(n), the nth triangular number, is \[T(n) = \frac{(n)(n + 1)}{2}\] Challenge:…