REND LAKE COLLEGE BENTON HIGH SCHOOL MATH 1109 PLANE TRIGONOMETRY

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1 REND LAKE COLLEGE BENTON HIGH SCHOOL MATH 1109 PLANE TRIGONOMETRY I. PREREQUISITE: MATH 1108 with a C or better. II. COURSE DESCRIPTION: A course dealing with definitions of trigonometric functions, graphing, formulas, identities, solution of triangles using trigonometric functions and logarithmetric functions, solution of trigonometric equations, inverse trigonometric functions and their graphs, complex numbers and the solution of practical problems. III. CREDIT: Total Credit Hours=3 Lecture 3 hours. IV. MATERIALS REQUIRED: Text: Algebra and Trigonometry, 4th Edition; Beecher. Pearson Publishing. Recommended: scientific calculator or graphing calculator V. EXPECTED OUTCOMES FOR STUDENT LEARNING: Upon successful completion of the course, the student will be able: A. to use the definitions of trigonometric functions. B. to solve right triangles. C. to use the Law of Sines, including the ambiguous case, and Law of Cosines to solve triangles. D. to prove identities. E. to use inverse trigonometric functions to solve problems and graph these inverse functions. F. to use vectors to solve application problems. G. to solve exponential equations. H. to solve logarithmic equations. I. to work with logarithmic functions using all bases, but particularly the common logarithm base of 10 and the natural logarithm base of e. J. to work with complex numbers; find the roots of complex numbers, graph the complex numbers, add, subtract, multiply, and divide complex numbers. K. to graph any of the six trigonometric functions using the amplitude, period and phase shift of the function.

2 VI. ASSESSMENT OF STUDENT LEARNING: This is not a departmentally assessed course. VII. INSTITUTIONAL OUTCOMES: Rend Lake College has adopted four essential learner outcomes, fundamental learning objectives embedded in every program of study, that all degree-completing students should be able to demonstrate. They are as follows: Critical Thinking: Demonstrate the ability to think in a self-directed, reflective manner when understanding, evaluating, and solving problems. Problem-Solving: Demonstrate the ability to resolve computational problems. Oral Communication: Demonstrate the ability to communicate clearly, concisely, and effectively through verbal and non-verbal language. Written Communication: Demonstrate the ability to communicate clearly, concisely, and effectively through written language. VIII. COURSE OUTLINE: A. Basics 1. Angles, Definition of 2. Angles and Similar Triangles 3. Definitions of Trigonometric Functions 4. Trigonometric Functions of Angles 5. Values of Trigonometric Functions 6. Radian Measure 7. Circular Functions 8. Linear and Angular Velocity 9. Vectors B. Right Triangle Trigonometry 1. Solving Triangles 2. Solving Applications using Vectors C. Graphing 1. Graphs of the Six Trigonometric Functions including changes in the Amplitude, Period, and Phase Shift (The six trigonometric functions are: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent) 2. Graphs of Composite Functions 3. Graphs of Complex Numbers 4. Graphs of Inverse Functions 5. Graphs of Vectors D. Trigonometric Identities 1. Fundamental Identities 2. Verify Identities 3. Sum and Difference Identities 4. Multiple-Angle Identities 5. Sum and Product Identities E. Trigonometric Equations 1. Inverse Trigonometric Functions 2. Trigonometric Equations a. with single angles b. with multiple angles

3 c. with phase shifts in the angles 3. Inverse Trigonometric Equation F. Applications of Trigonometry 1. Right Triangle Applications 2. Oblique Triangles and the Law of Sines, including the Ambiguous Case 3. The Law of Cosines 4. Vectors and Their Application 5. Trigonometric Form of Complex Numbers 6. De Moivre's Theorem and nth Roots 7. Operations on Complex Numbers: Addition, Subtraction, Product, and Quotient G. Exponential and Logarithmic Functions 1. Exponential Functions 2. Logarithmic Functions including a. common logarithm base of 10 b. natural logarithm base of e c. other bases 3. Evaluating Logarithms 4. Exponential and Logarithmic Equations 5. Applications using Exponential Growth and Decay and Compound Interest IX. ACADEMIC INTEGRITY: This class is subject to the college s Academic Integrity policy. All submitted work must be your own. Cheating or Plagiarism will not be tolerated. Any student found in violation of this policy will be subject to disciplinary action as outlined by RLC s Academic Integrity policy. X. ADDITIONAL INFORMATION: Contact Information: Molly Whaley, BCHS Math Dept. mwhaley@bentonhighschool.org (618) ext. 233 METHOD OF EVALUATING STUDENT S WORK: Unit exams, quizzes and/or homework assignments, computer assignments, final exam Grading Scale: % = A 80-89% = B 70-79% = C 60-69% = D Below 60% = E

4 Week 1: 6.1 Trigonometric Functions of Acute Angles Week 2: 6.2 Applications of Right Triangles 6.3 Trigonometric Functions of Any Angle Week 3: 6.4 Radians, Arc Length, and Angular Speed Review Test Week 4: 6.5 Circular Functions: Graphs and Properties Week 5: Quiz 1 Unit Circle pt 1 MATH 1109 College Trigonometry Course Outline Week 6: Quiz 2 Unit Circle pt Graphs of Transformed Sine and Cosine Functions Week 7: Review Test Week 8: 7.1 Identities: Pythagorean and Sum and Difference Week 9: 7.2 Identities: Cofunction, Double-Angle, and Half-Angle Quiz 3 Trigonometric Identities (7.1 & 7.2) Week 10: 7.3 Proving Trigonometric Identities 7.4 Solving Trigonometric Identities Week 11: Chapter 7 Review Test 3 Chapter 7 Test Week 12: 8.1 The Law of Sines 8.2 The Law of Cosines Quiz 4 Laws of Sines & Cosines (8.1 & 8.2)

5 Week 13: 8.3 Complex Numbers: Trigonometric Form 8.5 Vectors & Applications 8.6 Vector Operations Week 14: Chapter 8 Review Test 4 Chapter 8 Test Week 15: 5.2 Exponential Functions & Graphs 5.3 Logarithmic Functions & Graphs 5.4 Properties of Logarithmic Functions Week 16: 5.5 Solving Exponential Equations & Logarithmic Equations Review Test Week 17: 5.6 Applications & Models: Growth and Decay; Compound Interest Quiz Week 18: Final Exam Review Final Exam