MAT1093
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Precalculus
1093. Precalculus. (30) 3 Credit Hours. (TCCN = MATH 2312)
Prerequisite: MAT 1073 or the equivalent course or satisfactory performance on a placement examination. Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre’s theorem, and polar coordinates. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: DL01 $75; LRC1 $12; LRS1 $45; STSI $21.
Lesson Plan
Date  Sections  Topics  Prerequisite Skills  Student learning outcomes 

Week 1  Orientation 


Week 1  1.3  Functions and their graphs 


Week 2  1.7  Onetoone functions  Section 1.3: Functions and their graphs  Determine when a function or its graph is onetoone 
Week 2  1.7  Inverse functions  Section 1.3: Functions and their graphs 

Week 2  2.1  Angles and their measure  Elementary geometry and terminology 

Week 3  2.2  Trigonometric Functions: Unit Circle Approach 


Week 3  2.3  Properties of the Trigonometric Functions 


Week 4  2.4  Graphs of the Sine and Cosine Functions 
 
Week 4  2.5  Graphs of the Tangent, Cotangent, Cosecant and Secant Functions  Finding Vertical asymptotes of rational functions  Graph the basic tangent, cotangent, secant and cosecant functions using key points, vertical asymptotes, and reciprocal identities, as needed 
Week 5  2.6  Phase shift and Applications  Graph sinusoidal functions of the form y = A sin (ωx – φ) + B and y = A cos (ωx – φ) using transformations and determine the amplitude, \abs(A), period, T, and phase shift, φ/ω  
Week 5  Test 1 Review Session. Common Test 1: Ch.1 and 2.  
Week 6  3.1  The inverse Sine, Cosine and Tangent functions 


Week 6  3.2  The inverse Secant, Cosecant and Cotangent functions 


Week 6  3.3A  Trigonometric equations involving a single trig function  Section A.4: Solving algebraic equations  Find exact solutions in the interval [0, 2π) and in general form for equations with single trig function 
Week 7  3.3B  Trigonometric Equations 


Week 7  3.4  Trigonometric Identities 

Prove simple identities using the fundamental identities and algebraic technics 
Week 8  3.5  Sum and Difference Formulas  Section 2.2: Trigonometric Functions: Unit Circle Approach 

Week 8  3.6A  Doubleangle formulas 
 
Week 8  3.6B  Halfangle formulas 
 
Week 9  3.7  ProducttoSum and SumtoProduct Formulas  Basic algebra and geometry  Use producttosum and sumtoproduct formulas 
Week 9 


Week 10  4.1  Right triangle definitions of trig functions and related applications 


Week 10  4.2  The Law of Sines 

Learn and use the Law of Sines to solve two cases of oblique triangles (ASA and SAA for case 1, and SAA for case 2, also known as the ambiguous case that can result in no solution, one solution or two solutions) and related applications questions including those with bearings 
Week 11  4.3  The Law of Cosines  Section 3.3: Trigonometric Equations  Use the Law of Cosines to solve the other two cases of oblique triangles (SAS for case 3 and SSS for case 4) and related applications questions including those with bearings 
Week 11  4.4  Area of a Triangle  Section A.2: Geometry Essentials 

Week 11  5.1  Polar Coordinates 


Week 11  5.2  Polar Equations and Graphs 

Graph simple polar equations by converting them to rectangular form and then use Algebra to graph this rectangular equations 
Week 11/12  5.3  The complex plane 


Week 12  5.3  DeMoivere’s Theorem  Section 2.2: Trigonometric Functions: Unit Circle Approach  Use the trigonometric form of complex numbers to multiply, divide, and raise them to natural powers 
Week 12 


Week 13  7.4  Logarithmic and Exponential Equations 

Find exact and approximate solution sets for exponential and logarithmic equations of any base, including those from application questions 
Week 14  7.6  Exponential growth and decay models 

Create and use exponential growth and decay models from two data points 
Week 14  7.6  Newton’s law of Cooling models  Section A4: Solving quadratic equations  Create and use exponential models based on Newton’s Law of Cooling 
Week 14  7.6  Logistic growth and decay models  Section A4: Solving quadratic equations  Use Logistic growth and decay models to find present and future values, and times for any future value 
Week 15  Common Final Exam Review  All topics covered during the semester 