Chapter 4

Chapter 5

Chapter 6

Chapter 7

The text used in Maesumi Precalculus Math 2312

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.

Section 4.1 - 4.2 (14 topics)

Section 4.1 Angles and Their Measure

Objective 1. Find Degree Measure

Objective 2. Find Radian 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.

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.

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.

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.