# Comprehensive Algebra 2 with Trig š

Next session on Dec 5, 2022

Hosted by Jose Roberto Cossich G

### Series Details

About

Hey guys! Along with my Geometry series, here's one for Algebra 2 and Trig! It's never too early/late to start learning, so why not join?

Prerequisites: Algebra 1; good grasp of quadratics (which you can learn concurrently if you haven't already).

We're going to be covering

-Polynomials

-Vectors

-Complex Numbers

-Rational Functions

-Exponents/Logarithms

-Function Transformations

-Linear Transformations using Matrices

-Types of triangles

-Right Triangle Trigonometry

-Unit Circle and Trigonometric Identities/Values

-Radians and Degrees

-Trigonometric Functions

-Inverse Trigonometric Functions

-Sinusoidal Graphs/Equations

-Other Trigonometric Identities

ā ATTENDANCE POLICY

Attendance is optional but highly recommended since topics build on each other; however I understand that everyone has a busy schedule, so if you can't make it and want a catch-up session just ask!

Dates

November 14 - May 15

Learners

74 / 75

Total Sessions

25

### About the Tutor

Hi, my name's Jose, I'm a Junior and an international student. I love listening to Indie music, watching 80s movies, and reading in my spare time. I enjoy math because it allows me to express myself artistically, and tutor for the mere sake of those aha moments. I'm currently taking Calc 3 and AP Physics C, hope to see you soon!

### Upcoming Sessions

Session 3

#### Polynomial factorization

-Learn how to apply polynomial division in addition to the remainder and factor theorems to find the linear factors of polynomials

-Proving the factor and remainder theorem, and applying them to prove factors of a polynomial

Session 4

#### Review

-Reviewing quadratic factorization

-Learn about the features of polynomials represented visually in graphs including factors (zeros), the multiplicity of their zeros, the graphs y-intercept, and end behavior (odd or even or none).

Hey guys, today we will review the concepts in our first unit, polynomials. We will be focused more on practicing our skills and resolving any remaining doubts.

Session 5

#### Trigonometry

Hey guys,

Today we're going to learn the trigonometric ratios (SOHCAHTOA), reciprocal ratios, and build some intuition around them (it would be helpful to know about Similarity beforehand). We'll find the lengths of missing sides of right triangles, learn about complementary angles, and do some other practice.

Session 6

#### Complex numbers

Hey guys, these two sessions will be on Vectors, but I put it as about Complex Numbers because their relation will lay the foundations for our understanding of Complex Numbers.

- What is a Vector? What are n-vectors?

-Zero vectors

-Vector quantities vs Scalar quantities

-Finding the x and y component of a vector, adding and subtracting vectors together (the parallelogram rule

-The argument and modulus of a vector, what they are and how to derive them (inverse trig functions) -Some more advanced problems on vectors from Khan Academy

Session 7

#### Complex numbers

(CONTINUING)

Hey guys, these two sessions will be on Vectors, but I put it as about Complex Numbers because their relation will lay the foundations for our understanding of Complex Numbers.

- What is a Vector? What are n-vectors?

-Zero vectors

-Vector quantities vs Scalar quantities

-Finding the x and y component of a vector, adding and subtracting vectors together (the parallelogram rule -The argument and modulus of a vector, what they are and how to derive them (inverse trig functions) -Some more advanced problems on vectors from Khan Academy

Session 8

#### Complex numbers

Hey guys, today we will begin to cover Complex Numbers

-What they are,

-Complex solutions to quadratics,

-Factoring by sum of squares (and solving for the complex roots of polynomials using sum of squares),

-De Moivre's Theorem

-Euler's Formula

Session 9

#### Complex numbers

Hey guys, today we're going to find all the complex solutions to polynomials in general (not just through sum of squares or in quadratics) by covering

-Rectangular Form of Complex numbers and converting it to

-Polar Form of Complex Numbers

- The Imaginary Plane

-The Argument and Modulus of Complex Numbers.

Session 10

#### Complex numbers

(CONTINUING LAST SESSION)

Hey guys, today we're going to find all the complex solutions to polynomials in general (not just through sum of squares or in quadratics) by covering

-Rectangular Form of Complex numbers and converting it to

-Polar Form of Complex Numbers

- The Imaginary Plane

-The Argument and Modulus of Complex Numbers.

Session 11

#### Review

Hey guys, today we will review the concepts in our second unit, complex numbers. We will be focused more on practicing our skills and resolving any remaining doubts.

Session 12

#### Trigonometry

We're starting our Trigonometry Unit!

We're going to start with a brief series overview, then get into

-Types of Triangles

-Angle Properties

-The Triangle Inequality Theorem

-The Pythagorean Theorem -Review of SOHCAHTOA

Session 13

#### Trigonometry

Hey guys, today we're going to go over the law of sines and cosines (and their proofs) to find the missing sides of arbitrary triangles (and provide some more intuition to some congruence theorems using these laws)

Session 14

#### Trigonometry

Hey guys, today we'll learn what radians are and how to convert between them and degrees. Then we'll go over the Unit Circle, trig identities/values that we can derived from the unit circle, and then we'll practice computing trig values.

As always, catch-up sessions are available.

Session 15

#### Trigonometry

Hey guys, today we'll learn what radians are and how to convert between them and degrees. Then we'll go over the Unit Circle, trig identities/values that we can derived from the unit circle, and then we'll practice computing trig values.

As always, catch-up sessions are available.

Session 16

#### Trigonometry

Hey guys, today we're going to be plotting the values of trigonometric functions that we derived using the unit circle onto a graph; then we'll play around with inverse functions and make the trigonometric functions invertible (For background knowledge on making functions invertible, go to https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:invertible/a/intro-to-invertible-functions). We'll also determine the domain and range of these inverse functions and see their graphs as well.

As always, catch-up sessions are available.

Session 17

#### Trigonometry

Hey guys, today we're going to take a look at the features of sinusoidal (sine and cosine) functions today: amplitude, period, midline, and phase shift, and how each of these features corresponds to a different part of the sinusoidal equation af(b(x+c))+d, where f is either sin or cosine.

As always, catch-up sessions are available.

Session 18

#### Trigonometry

Today we'll just practice what we learnt last session, deriving the equations of sinusoidal functions using their graphs. This is a very tedious process, so we will have an additional session on this.

As always, catch-up sessions are available.

Session 19

#### Trigonometry

(CONTINUING)

Today we'll just practice what we learnt last session, deriving the equations of sinusoidal functions using their graphs. This is a very tedious process, so we will have an additional session on this.

As always, catch-up sessions are available.

Session 20

#### Trigonometry

Today we're going to be applying trig identities to solve sinusoidal equations!

Have fun, see you soon.

As always, catch-up sessions are available.

Session 21

#### Exponential models

Hey guys, today we're going to be covering

-Properties of exponents (rational exponents as well) (review)

-Exponential function properties (growth and decay)

Session 22

#### Logarithms

-What logarithms are and converting expressions into exponential/logarithmic form

-Logarithm properties

- Logarithmic functions

Session 23

#### Review

- Logarithm properties (review), proofs, and graphs.

- Unit review

Session 24

#### Transformations of functions

Hey guys, today we're going to be doing something different. We'll be play with different functions on desmos to build some intuition on...

-Vertical and horizontal translations

-Vertical and horizontal stretches/compressions

-Reflections

Session 25

#### Transformations of functions

Hey guys!

Today we'll cover matrices--what they are, how to add and subtract them, as well as multiply them.

We'll use this to prove the rotation matrix, a linear function to rotate functions or points by a given angle.