09.18.2018: One Lesson of Math

Today's soundtrack is Haircuts for Men: Solo Works Discography 1982-2016, a chill v a p o r w a v e album that's perfect for homework.

I'm bypassing the Randomizer's activity today; I want to start off my math course on a good foot, so this afternoon I'll be doing a quick review of what I learned in my recently-completed math course before I start the assignments for this semester's course.

Trigonometry calculator practice sheet

  • If I know the angle's degrees, I use the standard function (SIN, COS, or TAN); if I want to find the angle, I need to use the "2nd" button to use the inverse ratio to find the answer.

Introduction to Trigonometry

  • Relative to each corner on a right triangle, there are three sides

  • Hypotenuse

  • Opposite

  • Adjacent

  • There are three ratios used in trigonometry:

  • SINE (SIN)

  • Sine = opposite over hypotenuse


  • Cosine = adjacent over hypotenuse


  • Tangent = opposite over adjacent

  • To find an angle with Tangent, we need to use the inverse ratio, which is used on the TI-83 Plus by hitting the "2nd" key before choosing the desired ratio (e.g., "2nd, Tan" = "Inverse Tan")

  • If I know that my opposite is 3" and my adjacent is 4" and I want to find how many degrees this angle is, I would calculate Inverse Tan (3/4) = 36.87 degrees.

  • To calculate a length with Tangent, we need to know the degrees of one angle, and the length of either the opposite or adjacent side. Let x represent unknown side

  • Tan = O/A

  • Tan 20 degrees / 1 = 3.5" / x cross-multiply

  • Tan 20 (x) = 3.5, divide both by Tan 20 to isolate x

  • x = 3.5/Tan 20

  • Use calculator: 3.5 divided by Tan(20) = 9.6cm

Factoring Trinomials using Decomposition

  • x²+x-6

  • Need to find two numbers that produce the first term times the last term and also are the sum of the middle term: in this case, our product needs to be -6, and our sum needs to be 1. -2+3 equals 1; -2 times 3 = -6. Now we know that our middle term can be broken apart into those two numbers, and we rewrite our equation: x²-2x+3x-6.

  • Now we split that equation in half and take out common terms. In the first half, "x" is common; in the second half, 3 is common. We rewrite again, and this time put the common factors outside of brackets separating the two sides of the equation: x(x-2)+3(x-2).

  • We combine the two numbers outside of the brackets (x+3) and one set of the identical sets of numbers inside the brackets (x-2) and we have our final answer: (x+3)(x-2)!