Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7

John Turner Video Lectures for Precalculus 1ed by Julie Miller and Donna Gerken,
The text used in Maesumi Precalculus Math 2312

Chapter 3 Exponential and logarithmic functions

Section 3.1 - 3.3 (23 topics)

Section 3.1 Inverse functions
Objective 1. Identify one-to-one functions
Objective 2. Determine whether two functions are inverses
Objective 3. Find the inverse of a function
Video 001 Objective 1, horizontal line test
Video 002 Objective 2, inverse functions, composition of inverses
Video 003 Objectives 2+3, finding inverses, many-to-one functions

Section 3.2 Exponential functions
Objective 1. Graph exponential functions
Objective 2. Evaluate the exponential function base e
Objective 3. Use exponential functions to compute compound interest
Objective 4. Use exponential functions in applications
Video 004 Objective 1, exponential functions, graph, domain, range, asymptote
Video 005 Objectives 1+2, transformation of graph of exponential functions, natural base e
Video 006 Objectives 3+4, applications of exponentials, compound interest, radioactive carbon dating, half life

Section 3.3 Logarithmic functions
Objective 1. Convert between logarithmic and exponential forms
Objective 2. Evaluate logarithmic expressions
Objective 3. Apply basic properties of logarithms
Objective 4. Graph logarithmic functions
Objective 5. Use logarithmic functions in applications
Video 007 Objectives 1+2, converting between logarithmic and exponential forms
Video 008 Objectives 2+3+4, evaluating, basic properties, graphs, common and natural log
Video 009 Objectives 4+5, transformation of graph, domain, asymptote, applications, Richter scale for earthquakes

Section 3.4 - 3.5 (13 topics)
Section 3.4 Properties of logarithms
Objective 1. Apply the Product, Quotient, and Power Properties of Logarithms
Objective 2. Write a Logarithmic Expression in Expanded Form
Objective 3. Write a Logarithmic Expression as a Single Logarithm
Objective 4. Apply the Change-of-Base Formula
Video 010 Objectives 1+2, Applying the laws of logarithms and writing logarithmic expressions in expanded form.
Video 011 Objective 3, Writing a logarithmic expression as a single logarithm.
Video 012 Objective 4, Using the change-of-base formula for logarithms.

Section 3.5 Exponential and Logarithmic Equations and Applications
Objective 1. Solve Exponential Equations
Objective 2. Solve Logarithmic Equations
Objective 3. Use Exponential and Logarithmic Equations in Applications
Video 013 Objective 1, Solving Exponential equations.
Video 014 Objective 2, Solving Logarithmic equations.
Video 015 Objective 3, Solving logarithmic equations and applications of logarithmic and exponential equations.

NOTICE: 3.6 is Optional
Section 3.6 Modeling with Exponential and Logarithmic Functions
Objective 1. Solve Literal Equations for a Specified Variable
Objective 2. Create Models for Exponential Growth and Decay
Objective 3. Apply Logistic Growth Models
Objective 4. Create Exponential and Logarithmic Models Using Regression
Video 016 Objectives 1+2, Solving literal equations involving exponential expressions and logarithmic expression and an application of exponential growth/decay.
Video 017 Objective 2, Solving exponential growth/decay applications.
Video 018 Objectives 2+3, Exponential growth/decay example and rewriting an exponential expression into a natural base exponential expression.
Video 019 Objective 3, Applying logistic models.

Chapter 4 Trigonometric Functions

Section 4.1 - 4.2 (14 topics)
Section 4.1 Angles and Their Measure
Objective 1. Find Degree Measure
Objective 3. Determine Coterminal Angles
Objective 4. Compute Arc Length of a Sector of a Circle
Objective 5. Compute Linear and Angular Speed
Objective 6. Compute the Area of a Sector of a Circle
Video 020 Objective 1, Angles and their degree measure.
Video 021 Objective 1, Angles and their radian measure.
Video 022 Objectives 2+3, Coterminal angles and their radian measure, arc length.
Video 023 Objectives 4+5+6. Computing linear and angular speed and the area of a sector of a circle.

Section 4.2 Trigonometric Functions Defined on the Unit Circle
Objective 1. Evaluate Trigonometric Functions Using the Unit Circle
Objective 2. Identify the Domains of the Trigonometric Functions
Objective 3. Use Fundamental Trigonometric Identities
Objective 4. Apply the Periodic and Even and Odd Function Properties of Trigonometric Functions
Objective 5. Approximate Trigonometric Functions on a Calculator
Video 024 Objective 1. Introduction to the six trig functions based on the unit circle.
Video 025 Objectives 1+2. To evaluate trigonometric functions using the unit circle and to identify the domains of the six trig functions.
Video 026 Objectives 3+4. The reciprocal, quotient, and Pythagorean identities.
Video 027 Objective 4. Applying periodic and even / odd properties of trigonometric functions.

Sections 4.3 - 4.4 (16 topics)
Section 4.3 Right Triangle Trigonometry
Objective 1. Evaluate Trigonometric Functions of Acute Angles
Objective 2. Use Fundamental Trigonometric Identities
Objective 3. Use Trigonometric Functions in Applications
Video 028 Objective 1. Defining the trigonometric functions of acute angles using a right triangle.
Video 029 Objectives 2+3. Fundamental trig identities and using trig functions in applications.

Section 4.4 Trigonometric Functions of Any Angle
Objective 1. Evaluate Trigonometric Functions of Any Angle
Objective 2. Determine Reference Angles
Objective 3. Evaluate Trigonometric Functions Using Reference Angles
Video 030 Objectives 1+2. Evaluating trig functions of any angle and introducing the reference angle.
Video 031 Objectives 2+3. Determining reference angles and evaluating trig functions using reference angles.
Video 032 Objectives 2+3. Determining reference angles and evaluating trig functions using reference angles.

Sections 4.5 - 4.7 (17? topics)
Section 4.5 Graphs of Sine and Cosine Functions
Objective 1. Graph y = sin x and y = cos x
Objective 2. Graph y = A sin x and y = A cos x
Objective 3. Graph y = A sin Bx and y = A cos Bx
Objective 4. Graph y = A sin(Bx - C) + D and y = A cos(Bx - C) + D
Objective 5. Model Sinusoidal Behavior
Video 033 Objective 1. An introductory look at the graphs of y=sin x and y=cos x.
Video 034 Objective 2. An introductory look at the graphs of y= A sin x and y= A cos x.
Video 035 Objectives 3+4, Graphing y=Asin Bx and y=Acos Bx. Introducing the phase shift.
Video 036 Objective 4, To graph sine and cosine functions with multiple transformations.
Video 037 Objective 5, Graph of a sine with multiple transformations, and an application.

Section 4.6 Graphs of Other Trigonometric Functions
Objective 1. Graph the Secant and Cosecant Functions
Objective 2. Graph the Tangent and Cotangent Functions
Video 038 Objective 1, To introduce the graphs of the cosecant and secant functions.
Video 039 Objective 1, Graphing transformations of the secant and cosecant functions.
Video 040 Objective 2, Graphing the tangent and cotangent functions
Video 041 Objective 2, Transformations of tangent and cotangent.

Section 4.7 Inverse Trigonometric Functions
Objective 1. Evaluate the Inverse Sine Function
Objective 2. Evaluate the Inverse Cosine and Tangent Functions
Objective 3. Approximate Inverse Trigonometric Functions on a Calculator
Objective 4. Compose Trigonometric Functions and Inverse Trigonometric Functions
Objective 5. Apply Inverse Trigonometric Functions
Objective 6. Evaluate the Inverse Secant, Cosecant, and Cotangent Functions
Video 042 Objectives 1+2, Introduction to the inverse sine and cosine functions.
Video 043 Objectives 2+3, Introduction to the inverse cosine and tangent functions.
Video 044 Objectives 4+5+6, Composing trig functions and inverse trig functions, applying inverse trig functions, and evaluating the inverse secant, cosecant, and cotangent functions.

Chapter 5. Analytic Geometry

Sections 5.1 - 5.2 (13 topics)
Section 5.1 Fundamental Trigonometric Identities
Objective 1. Simplify Trigonometric Expressions
Objective 2. Verify Trigonometric Identities
Objective 3. Write an Algebraic Expression as a Trigonometric Expression
Video 045 Objective 1, Introducing the fundamental trig identities to simplify trig expressions.
Video 046 Objective 2, Verifying trig identities.
Video 047 Objective 2, More verifying trig identities.
Video 048 Objective 3, To write algebraic expressions as trig expressions.

Section 5.2 Sum and Difference Formulas
Objective 1. Apply the Sum and Difference Formulas for Sine and Cosine
Objective 2. Apply the Sum and Difference Formulas for Tangent
Objective 3. Use Sum and Difference Formulas to Verify Identities
Objective 4. Write a Sum, A sin x + B cos x , as a Single Term
Video 049 Objective 1, Sum and difference formulas for sine and cosine .
Video 050 Objectives 2+3+4, Applying the sum and difference formulas for tangent, using the sum and difference formulas to verify identities, and writing a sum of A sin x and B cos x as a single term.

Sections 5.3 - 5.4 (6 topics)
Section 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
Objective 1. Apply the Double-Angle Formulas
Objective 2. Apply the Power-Reducing Formulas
Objective 3. Apply the Half-Angle Formulas
Video 051 Objective 1, Sum and difference formulas for sine and cosine .
Video 052 Objectives 2+3, Introducing power reducing and half angle formulae.

Section 5.4 Product-to-Sum and Sum-to-Product Formulas
Objective 1. Apply the Product-to-Sum Formulas
Objective 2. Apply the Sum-to-Product Formulas
Video 053 Objectives 1+2, Introducing the product-to-sum and sum-to-product formulas and applications.

Section 5.5 (22? topics)
Section 5.5 Trigonometric Equations
Objective 1. Solve Trigonometric Equations in Linear Form
Objective 2. Solve Trigonometric Equations Involving Multiple or Compound Angles
Objective 3. Solve Higher-Degree Trigonometric Equations
Objective 4. Use Identities to Solve Trigonometric Equations
Objective 5. Use Inverse Functions to Express Solutions to Trigonometric Equations
Objective 6. Approximate the Solutions to Trigonometric Equations on a Calculator
Video 054 Objectives 1+2, Solving trig equations in linear form and involving multiple or compound angles.
Video 055 Objectives 3+4, Solving higher-degree trigonometric equations and using identities to solve trigonometric equations.
Video 056 Objective 5, Solving trigonometric equations using the inverse trig feature on a scientific or graphing calculator.
Video 057 OPTIONAL, Objective 6, Approximating solutions to trigonometric equations using a graphing calculator.

Chapter 6. Applications of Trigonometric Functions

Section 6.1 (6 topics)
Section 6.1 Applications of Right Triangles
Objective 1. Solve a Right Triangle
Objective 2. Solve Applications of Right Triangles
Objective 3. Compute the Bearing of an Object
Video 058 Objectives 1+2, Solving right triangles and introducing applications of right triangles.
Video 059 Objectives 2+3, To solve applications involving right triangles and bearings.

Sections 6.2 - 6.3 (8 topics)
Section 6.2 The Law of Sines
Objectives 1. Solve a Triangle Using the Law of Sines (SAA or ASA)
Objectives 2. Solve a Triangle Using the Law of Sines (SSA) Ambiguous Case
Objectives 3. Compute the Area of a Triangle Given SAS
Objectives 4. Apply the Law of Sines
Video 060 Objective 1, Introduction to using the law of sines to solve oblique triangles.
Video 061 Objective 2, The ambiguous case of the law of sines.
Video 062 Objective 3, Computing the area of a triangle given SAS and applying the law of sines.

Section 6.3 The Law of Cosines
Objective 1. Solve a Triangle Using the Law of Cosines (SAS)
Objective 2. Solve a Triangle Using the Law of Cosines (SSS)
Objective 3. Apply the Law of Cosines
Objective 4. Use Heron’s Formula to Compute the Area of a Triangle (OPTIONAL)
Video 063 Objectives 1+2, Using the Law of Cosines to solve an oblique triangle, given two sides and the included angle or given the three sides.
Video 064 Objectives 3+4, Applications of the law of cosines and Heron's Formula.

Chapter 7. Trigonometry Applied to Polar Coordinate Systems and Vectors

Sections 7.1 - 7.2 (11 topics)
Section 7.1 Polar Coordinates
Objective 1. Plot Points Using Polar Coordinates
Objective 2. Convert Ordered Pairs Between Polar and Rectangular Coordinates
Objective 3. Convert Between Equations in Polar and Rectangular Coordinates
Video 065 Objective 1, Introduction to polar coordinates and graphing points in polar coordinates.
Video 066 Objective 2, Converting between polar and rectangular coordinates.
Video 067 Objectives 2+3, Converting between polar and rectangular equations.

Section 7.2 Graphs of Polar Equations
Objective 1. Graph Polar Equations by Plotting Points
Objective 2. Test Polar Equations for Symmetry
Objective 3. Categorize Polar Equations and Their Graphs
Video 068 Objective 1, Introduction to graphing a polar equation.
Video 069 Objective 2, Symmetry of polar graphs .
Video 070 Objectives 2+3, Examples of polar graphs and names of common polar graphs.