## 04.29.2019: One Lesson of Math - Studying, Part 1

Today's soundtrack is Long-view: Mercury, a nice rock album. It reminds me a lot of a less-proggy Blackfield. Today is dedicated to studying. I'm feeling pretty overwhelmed right now; all of the identities and methods are blending together. Units 5 and 6, which my upcoming test covers, were both quite large, and covered a lot of material. I'm doing my best to ensure I retain the major concepts without getting bogged too much. My game plan is to review the unit quizzes, review

## 04.28.2019: One Lesson of Math - Trigonometric Equations and Identities, 6/6: Double Angle Identitie

Today's soundtrack is Behemoth: Demigod, a death metal album with dark lyrics based on themes found in ancient folklore and religions. This afternoon, I'm working on the last lesson in this unit; this unit is the last unit in this module; so I'll be writing my third of the four module tests this week. This unit deals with Double Angle Identities. These tell us what happens if both a and b are equal to θ. There are three categories of double angle identities: sin, cos, and tan

## 04.27.2019: One Lesson of Math - Trigonometric Equations and Identities, 5/6: Sum and Difference Ide

Today's soundtrack is Gojira: L'Enfant Sauvage, a metal album that is heavier than four hundred million suns. So I mentioned yesterday that I was having trouble figuring out what to do with trig identities with coefficients. I got some help from a friendly Redditor and was able to finally overcome the challenge. It turns out that the problem was never with the coefficients, but the fact that I entirely overlooked the fact that "1" needed to be rewritten into its Pythagorean f

## 04.26.2019: One Lesson of Math - Catching Up

Today's soundtrack is Amon Amarth: Twilight of the Thunder God, an epic viking-themed melodic death metal album. This evening, I'm catching up on the assignments from the last two lessons, which were on the trigonometric identities, then I'm doing a quiz. Links to the previous lessons: Part 1, Part 2. I'm having quite a bit of difficulty with the assignment. The problems that I'm being asked to solve are a fair bit more complex than those in the lessons, and there are added c

## 04.25.2019: Trigonometric Equations and Identities, 4/6: Trigonometric Identities, Part 2

Today's soundtrack is Taylor Swift: 1989, the album that marked her switch from country pop to...pop-pop. It's such a great album - very catchy! Today, I'm continuing to learn about trigonometric identities. I was introduced to an important rule today that will really streamline the process of proving identities: We should only multiply terms if doing so will cancel a factor. We can use Difference of Squares factoring to break down a term so that we can prove an identity. Fo

## 04.24.2019: One Lesson of Math - Trigonometric Equations and Identities, 3/6: Trigonometric Identit

Today's soundtrack is Dream Theater: Falling Into Infinity, probably their most radio-friendly album. You may have noticed that this series is titled "Trigonometric Equations and Identities." So far, we've been working with equations; today, we'll be learning about trigonometric identities. Let's start by differentiating the two. An equation is only true for certain values of its variables. An identity is true for any values of its variables. The following are the identities

## 04.23.2019: One Lesson of Math - Trigonometric Equations and Identities, 2/6: Solving Trigonometric

Today's soundtrack is Petra: Petra Means Rock, a compilation album that includes many of the hits from their earlier albums. This afternoon, I'm learning how to solve trig equations without using a calculator. Trigonometric equations include a trig function and a variable - for example, y = sin x. How to solve first-degree trigonometric equations for exact values Isolate the trigonometric function Using absolute values of the equation, refer to the special triangles and find

## 04.22.2019: One Lesson of Math - Trigonometric Equations and Identities, 1/6: Solving Trigonometric

Today's soundtrack is Christafari: Valley of Decision, a reggae album that I've loved since I first got the album from a high school friend. Today, I'm learning how to use technology to solve trigonometric equations. I started the lesson by watching this video, which covered the two basic ways of solving trig equations that equal each other (graphing them as two separate functions, or moving everything onto one side so that y = 0 and finding the zeros). But let's back up a bi

## 04.22.2019: Circular Functions Unit Test

Today's soundtrack is Monastic Choir of the Valaam Monastery: The Athos of the North, a gorgeous Russian Orthodox album filled with beautiful harmonies as the singers chant spiritual hymns. This afternoon, I'm studying for - and then writing - my unit test on circular functions. To study for the unit test, I practiced drawing a unit circle, reviewed the special triangles and the graph that they build, then reviewed the quizzes that I've done in this unit. I was able to draw t

## 04.21.2019: One Lesson of Math - Circular Functions, 10/10: Graphing the Trigonometric Reciprocal Fu

Today's soundtrack is Runaway City: Armored Heart, a solid alt-rock album. I don't know why we never heard more from this band; my only guess is that they were a bit too late hopping onto the post-grunge train. This afternoon, I'm learning how to graph the reciprocal functions. The reciprocal trigonometric ratios are: Cosecant Reciprocal of Sine Written "csc" cscθ = (1 / sinθ) Secant Reciprocal of Cosine Written "sec" secθ = (1 / cosθ) Cotangent Reciprocal of Tangent Written

## 04.20.2019: One Lesson of Math - Circular Functions, 9/10: Graphing the Tangent Function

Today's soundtrack is Relient K: ᚎ Score and Seven Years Ago, a pop-punk album that is probably the most introspective material that I've heard Relient K release yet. We've learned how to graph the sine and cosine functions. Now, we're learning how to graph the tangent function. The tan graph is made up of multiple vertical asymptotes, between each of which exists a line that starts in negative infinity near the left asymptote, has a point of inflection that is located on the

## 04.19.2019: One Lesson of Math - Circular Functions, 8/10: Modelling Real Situations Using Sinusoida

Today's soundtrack is Dream Theater: Dream Theater, their self-titled album that was the first to feature Mike Mangini writing the drum parts. It's a great album; though it is a progressive metal album, it isn't very experimental; in my opinion, that fit the needs of the album well, and it is a very solid effort. I was surprised at the simplicity of the album art; many of their other albums have multi-faceted pieces of art. This afternoon, I'm learning about ways that we can

## 04.18.2019: One Lesson of Math - Catching Up

Today's soundtrack is White Zombie: La Sexorcisto: Devil Music Vol. 1, a rock project featuring Rob Zombie on vocals. I bought the album after seeing his film "The Devil's Rejects." This afternoon, my wife kept the kids occupied whlie I did a thorough house-cleaning, the afterglow of which I'm still basking in. I love having a clean house. This evening, I worked on the assignment portion of yesterday's lesson on sinusoidal functions with rational periods, then I wrote the qui

## 04.17.2019: One Lesson of Math - Circular Functions, 7/10: Sinusoidal Functions with Rational Period

Today's soundtrack is Lecrae: Rehab, a solid rap album with a positive message. So far, we've been working with functions whose periods were irrational. Today, we'll be learning about trigonometric functions with rational periods. In yesterday's lesson, we learned that we can determine the period of a trigonometric function by using the equation p=2π/b. But what happens if b is 2π/x? Well, we know that dividing a fraction by another fraction just requires that we multiply the

## 04.16.2019: One Lesson of Math - Circular Functions, 6/10: Transformations of Trigonometric Function

Today's soundtrack is The Everly Brothers: Bye Bye Love, a compilation of their hits. This morning, I'm continuing where we left off yesterday in learning about the various transformations that we can apply to trigonometric functions. So we already know how to phase shift (horizontally translate), change the amplitude (vertically expand or compress), and vertically displace (translate vertically). Now, we'll be learning how to expand or compress a trigonometric function horiz