Trig identity Three Ways (at least)
This post starts with reading elsewhere about someone struggling with the following trig identity given a triangle with three angles x, y, z show: $$ \tan{x}...
trigonometry
Ptolemy’s Theorem via a bit of Trig and similar triangles
Here’s a straightforward trigonometric proof of Ptolemy’s Theorem using scale factors and the Law of Cosines. First we start with a cyclic quadrilateral and…
Sine Hunt
Sine HuntThis is a working post to collect problems themed around sine. It all started during the last MathJam when a few came up: Criteria: only sine and ...
Trig Cheat Sheet Project
A few months ago, I saw a thread about writing a trigonometry cheat sheet for someone studying Pre-Calculus. I decided that I wanted to do a visual version ...
Pushing the limits
I’m still playing around with the ideas from going-one-step-beyond-herons-formula And this time I looked at a more complex problem. Overall the approach l...
Arctan Addition Formulas are really Sin/Cos angle addition Formulas in Disguise
An observation from this weekend
Trigonometric Pythagorean Relationships
Very short post today to illustrate something I’ve never considered before. Everyone usually has a diagram to illustrate the Pythagorean relationship on the...
Trig Angle Addition Two Ways
I’m really enjoying contrasting these two approach right now to deriving the since and cosine angle addition formulas. Just like in the normal pedagogy for t...
Heron’s Formula vs Trigonometry
This random pedagogical thought occurred to me today: Both Heron’s Formula and the Law of Cosines provide ways to find the area of a triangle with just its ...
Regular Heptagon puzzle walk through
There are too many wildly different an interesting ways to attack this problem to not document.
Roots of Unity: Pursuing Extra Roots
Background: This piece all started with my last post thinking about equalities of the form $ \cos (nx) = \cos(mx) $
Trigonometry Walk Through Three Ways
I saw the following trigonometry problem the other day and decided it would make another good walk through since it hits several themes I’ve been exploring.
Trig Walk Throughs
I’m in the process of writing a bigger piece on the role of trig formulas but I was looking for an example of their use during a geometry proof and came to t...
Reexamining the Law of Sines
I’ve been working my way through Geometry Revisited over the last few days and so far I’m really happy with the purchase.
Sometimes representation does matter
This is a small observation based on a post from @samjshah on the topic of the trig double angle formulas: