06.26.2018: One Lesson of Math

Today's soundtrack is Haken: Visions.

I've completed Basic Math & Pre-Algebra For Dummies, which was a personal goal that I'd set for myself before taking any teacher-led math courses. I'll be starting a month-long Foundations of Math and Precalculus course on July 3, so to prepare for that, I've signed up for two Khan Academy math modules, Algebra 1 and Precalculus, in the hopes that I will be better prepared for the course.

The Khan Academy Precalculus course begins by offering a quiz that they use to "identify your areas for growth [and] recommend lessons for exactly what you need to learn" (https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc), and says that it should take about 20 minutes.


So, that only took me five minutes. None of the questions that they asked looked like anything I've seen before (except maybe in pictures of scientists in front of chalkboards filled with equations). I had to skip every single question, so I'll be starting at the first lesson: "Solving basic sinusoidal equations." I watched the first video on it, and even that is talking about things I haven't yet learned. I think I've missed a step.


After doing some Googling on the subject, I've learned that the foundation needed for calculus is algebra and trigonometry. So I've started the Trigonometry module on Khan Academy instead.

Introduction to the Trigonometric Ratios

A right triangle's hypotenuse doesn't touch the right angle; it is the longest side. Its opposite side is "across from a given angle" (citation), and its adjacent side is the side that is not the hypotenuse that is "next to a given angle" (citation).

Trigonometry is "the study of the ratios of sides of triangles" (citation).

There are three functions of trigonometry: sine, cosine, and tangent (sin, cos, tan). These serve to "specify the ratios of certain sides" (citation).

We use the mnemonic "soh cah toa" to remember the following:

soh: Sin = Opposite over Hypotenuse

cah: Cos = Adjacent over Hypotenuse

toa: Tan = Opposite over Adjacent

That was a fun lesson; I look forward to the next one!