Good morning to the third quarter. First, we will review the unit circle. I will show the students how to find the sin, cos, tan values of the different parts of the unit circle. We will have a quiz on the unit circle next class. You will have to fill in a unit circle with degrees, radians, and coordinates. I will then review questions on 5.1. We will look over more proofs as a class. I will then introduce the angle sum formulas for sin, cos, tan. We will also look at inverse sin, cos, tan, and how to deal with the inverse trig functions within a problem. We will also go over how to find sin given cos and vice versa.

5.2 Sum and Difference Formulas

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quiz next class

First, we will have the unit circle quiz.  This should take about 10 minutes.  I will then go over any questions on the homework.  Now it’s time for the Double-Angle, Power-Reducing, and Half-Angle Formulas.   I will show the students how some of these formulas are created using  the sum and difference formulas.  I will then walk-through different examples that I’ve posted on the notes.   These examples should cover the objectives above.  I will have the students up to the board again next class working through these problems for homework.

5.3 HW - Double-Angle, Power-Reducing, and Half-Angle Formulas

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I will return the circle quizzes. We will then go over the 5.3 homework. I will pull students to the board to walk through the problems using the theorems that we have gone over the last couple of classes. We will look at how to use the new formulas to change equations and simplify.

5.4 HW - Product-to-Sum and Sum-to-Product Formulas

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            First, I will go over any questions on the homework.  Then we will review the unit circle.  I will then remind the students which coordinates are sin and cos.  I will also remind them how to find Tan.  We will look at the fact that there are sometimes multiply solutions. We will then look at the how to find these different solutions. We will then start looking at some trig equations and how to solve them.  I will review how students can apply algebra to solve these equations.  I have created a long note sheet of different problems that need to be solved.  There may be a quiz tomorrow on trig formulas.

5.5 HW - Trigonometric Equations

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Today we will have a quiz on the formulas for Chapter 5. I will give the class about 20 minutes to study for the quiz. There will be another quiz on Tuesday of next week that will involve proofs from chapter 5. After the quiz we will go over any questions on the homework. Todays homework is just a review of chapter 5.

Chapter 5 review

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First thing we will do is go over the quiz. I will walk the students through the formulas so that they can review them. I will then go over any questions on the Chapter 5 review homework. We need to figure out when we want to take the Chapter 4 and 5 tests.

I will then go over the law of sines. We will go through the proof for the law of sines. We will look at how to determine how many triangles will be formed by the given triangle values, and how to find the values of said triangles.

I will then go through the proof of the Area of triangles formula using sines. We will look at how to find the area of said triangles.

Lastly we will use the theorems that we went over today to solve word problems and real life situations.

Chapter 6.1 Law of sins

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Law of Sines Video

I'm supposed to be in a meeting from 9-10. I'm not sure that is the ending time, so I don't know when I will get to class. The class will be covered by someone from the office. When I get to class, we will look at the 6.1 homework. I will go over any questions on the law of sines, area of a triangle, and some word problems.

First, we will go over any questions on the homework.  I will then review the law of Sines and how they are used.  I will then introduce the law of Cosines and hopefully be able to show the students the proof.  There is a video attached, that has the proof. I will then go through how to use the law of cosines to solve triangles.  I will then solve a 3 sided triangle.  We will look at the area of the triangle as well, using the side angle side formula for area.  We will then use Heron’s formula and see if they match.  If there is extra time, we may have a quiz or start the homework. 
Need to find a day to take the chapter 4 test.

Chapter 6.2 Law of Cosines

Law of Cosines video

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Today I will be out on a field trip. We will have the Chapter 4 test on Thursday of next week. Today I'm providing a Chapter 4 review. You will be required to complete this assignment, and ask questions next class before the test. I will try and have the Quiz on all formulas next class, Tuesday Feb 11.

Chapter 4 review

Chapter 4 test next week

Quiz next class on all formulas

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Chapter 4 test next class

Chapter 4 test

Chapter 4 test

      First, we will go over any questions on the 6.2 homework.   We have already done this, but if anyone wants to review I will.   If you wish to challenge test answers I will try and find time today to review.  I will also be giving back the formula quiz today. 
            We will then look at polar coordinates.  This is just a new way of looking at rectangular coordinates.  I will show then students how to locate the angle and radius of a polar coordinate point.  I will then use triangles to show how polar coordinates and rectangular coordinates are the same. We will then look at polar equations and rectangular equations and how they are related.  I will graph both polar equations and rectangular equations on the same graph.  We will then look at ways to convert polar equations to rectangular equations and vice versa.

There maybe a quiz next class.

6.3 HW - Polar Coordinates

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            First, we will review the homework from last class.  We will then look at a polar equation and start plotting points.  We will look at how the graph looks based just on plotting points.  I will then have the students look for some symmetry in the graph.  Can the graph be folded over some line.  I will then introduce the symmetry formulas and show how they relate to the graph. 
            I will have the students use Desmos to look at how some of these graphs look.  The students will have to use polar graphs and plot points for some of the homework.  I will show them some key points to plug in to have a basic idea of the graph.

6.4 HW - Graphs of Polar Equations

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For at least 2 graphs I want tables (r, theta)

We need to take the chapter 5 test. Today you will have the Chapter 5 practice test. You will need to use all of the formulas you have learned in chapter 5. I will create the chapter 5 test from these questions. Go through them so that you have a clear understanding of them. We will go over any questions next class.

Chapter 5 practice test

We are gonna go over the homework and practice test

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test

First, we will go over any questions on any of the polar exercises.  I will then review what a complex number is and how to graph it.  We will then look at how to convert rectangular to polar and back again.  I will then review how to find the product and quotient of complex numbers.  We will then look at what happens when we raise complex numbers to exponents in polar form.  We will then use this knowledge to find roots of complex numbers.  I will walk the students through the theorems and how they can be applied.

6.5 Complex Numbers in Polar Form: DeMoivre’s Theorem

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            First, we will review the homework from last class.  There will be a quiz on 6.5 today.  I will then introduce a simple vector on a graph.  We will look at what it means to have vectors be equal and opposite.  We will look into scaler multiplication of vectors. We will look into solving vectors in the ai+bj form. We will use trig to find the vectors in Rectangular coordinates. I will then have the students walk through a situation where we will use vectors to mathematically model the situation.

6.6 Vectors

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First, we will review the homework on vectors. We may have a quiz on 6.6 vectors. We need to try and find some time to take a chapter 6 test.

Today we will be working on system of equations involving 2 variables. First, we will go over the number of solutions to a system of equations and what that looks like on a graph. We will look at how to determine if a point is part of a solution set. I will then review how to solve systems of equations using substitution, elimination, and substitution.

7.1 systems of equations 2 variables

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First, we will go over the homework. I will then go over any questions on chapter 6 that the class has. I would like to have a chapter 6 review and get ready for a test on Thursday of next week. We will go over the chapter 6 review next class (Tuesday). Then the test will be on Thursday.

Chapter 6 review (test next week, Thursday)

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SAT, won't see you guys.

Study for the Chapter 6 test

Go over the Chapter 6 review. We will then start section 7.4 (systems of non-linear equations).

            First, we will go over the homework from last class. I will then go over the basic shapes (not all) of non-linear systems and show graphically how many solutions are possible in different situations. We will then go through how to solve these systems using substitution, elimination, and graphing.  I will then show the students how to solve word problems.  First, we will draw the situation, then we will mathematically model the situation.  From there we will solve the system of equations that we have created.

I will then go over any questions the students have on the chapter 6 review. Any extra time will be used for quiz and test challenges.

go over the review for Chapter 6.

7.4 Systems of non linear equations (due after spring break)

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Test Chapter 6

            First, we will review the homework for 7.4.  I will also go over when any of the students that missed the Chapter 6 test can make it up.  We will discuss whether or not to fold Chapter 7 into Chapter 9 for the test.  I will then talk about what an ellipse looks like.  I will have ask the students where they think ellipse occur. We will talk about where in nature they see ellipses. I will then show them what the foci are for.  We will look at an ellipse drawing using the lanyard from my ID.  We will then look at the basic proof (if we have time).  I will then go into the formulas regarding ellipses.  I will show the class how to graph, find the foci, complete the square to create an ellipse equation.  I will then have the students start their work.

9.1 ellipses

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