TRI-COUNTY TECHNICAL COLLEGE

COURSE SYLLABUS

Course Prefix & Number:    MAT 111__________

Course Title:                          College Trigonometry

Class Hours                         Lab Hours                     Credits

Per week:  3.0                    Per Week:   0                  Awarded:  3.0

Catalog Description: This course includes the following topics:  circular functions; trigonometric identities; solution of right and oblique triangles; solution of trigonometric equations; polar coordinates; complex numbers, including Demoivre’s theorem; vectors; conic sections; sequences and series.

Entry Level Skills: 1)  Solve, graph, and use polynomial and rational functions over the real and complex fields.

                                 2)  Graph and apply exponential and logarithmic functions.

                                 3)  Solve systems of linear equations and inequalities.

Pre-requisites: MAT 110 with a grade of C or better.

Co-requisites: None

Text(s)/Required Materials: A Graphical Approach to Algebra and Trigonometry by John Hornsby, Margaret Lial, and Gary Rockswold, Fourth Edition, Pearson/Addison-Wesley, 2007

Equipment: Graphing calculator (TI-83, TI-83 Plus, TI 84 Plus, or TI-89 is recommended)

Course Competencies and Objectives/Major Course Topics:

Unit I: Trigonometric Functions

Upon completion of this unit (Sections 8.1-8.5) the student should be able to:

1.         Convert decimal degrees to minutes/seconds and vice versa.

2.         Define radian and convert the measure of an angle from degrees to radians and vice versa.

3.         Find arc length and area of a sector of a circle.

4.         Describe circular motion using angular and linear speed, and convert one to the other.

5.         Find the exact values of the trigonometric functions using a point on the terminal side of an angle.

6.         Determine properties of the trigonometric functions, such as domain and range, period, sign, even or odd.

7.         Find exact values of trigonometric functions using identities and properties.

8.         Define and evaluate the six trigonometric functions as ratios of the lengths of the sides of a right triangle.

9.         Find the exact trigonometric functions values for angles with reference angles of p/6=30°, p/4=45° and p/3=60°.

10.     Use a calculator to approximate values of trigonometric functions, and to find the measure of an angle using inverse functions.

11.     Solve right triangles (including applied problems) using right triangle trigonometry.

12.     Evaluate the six circular functions of a real number by hand, and using a calculator.

 Unit II:  Graphs of Circular Functions; Trigonometric Identities

 Upon completion of this unit (Sections 8.6-8.8 and 9.1-9.3) the student should be able to:

1.         Graph sine and cosine functions by identifying amplitude, period, horizontal and vertical translation.

2.         Graph basic transformations of cosecant, secant, tangent, and cotangent, functions.

3.         Give an equation that models simple harmonic motion, or analyze motion of a given model.

4.         State the following trigonometric identities from memory: basic, even-odd, Pythagorean, sum and difference, double-angle and half-angle.

5.         Simplify or rewrite trigonometric expressions using identities and algebraic manipulations.

6.         Verify that a given trigonometric equation is an identity, using algebraic manipulations as well as appropriate formulas.

7.         Find the exact numerical value of trigonometric expressions through the use of identities.

 Unit III:  Inverse Circular Functions, Solving Equations, and Analyzing Triangles

 Upon completion of this unit (Sections 9.4-9.6 and 10.1-10.2) the student should be able to:

1.         Define and find the exact value of the inverse trigonometric functions.

2.         Use a calculator to approximate inverse trigonometric function values.

3.         Find the exact value of expressions involving inverse trigonometric functions.

4.         Use identities, factoring, and basic algebraic methods to solve conditional trigonometric equations.

5.         Use a calculator/graphing utility to approximate solutions to trigonometric equations.

6.         Solve a trigonometric equation, and then use a graphing calculator to solve an associated inequality.

7.         Apply Law of Sines and Law of Cosines to solve for all unknown parts of a triangle.

8.         Solve applications from surveying, navigation, movement in a plane, etc. using oblique triangles.

9.         Use Heron’s Formula or the SAS formula to find the area of a triangle.

 Unit IV:  Vectors, Complex Numbers, and Polar Coordinates

 Upon completion of this unit (Sections 10.3-10.6) the student should be able to:

1.         Graph vectors, including sums, differences, and scalar multiples.

2.         Add and subtract, find scalar products, and determine magnitude of vectors algebraically.

3.         Use unit vectors and components to add and subtract, find scalar products, and determine magnitude of vectors.

4.         Find the dot product of two vectors and use the dot product to find the angle between two vectors.

5.         Write a vector in terms of (or using) its magnitude and direction.

6.         Solve applied problems involving vectors.

7.         Convert a complex number from rectangular form to trigonometric (polar form), and vice versa.

8.         Find products and quotients of complex numbers in polar form.

9.         Find powers of complex numbers using De Moivre’s theorem.

10.     Find n^th roots of a complex number.

11.     Convert polar coordinates to rectangular coordinates and vice versa.

12.     Plot points using polar coordinates.

13.     Graph polar equations by plotting points and using a graphing utility.

14.     Identify and graph  polar equations by converting to rectangular equations.

 Unit V:  Conic Sections and Parametric Equations

 Upon completion of this unit (Sections 6.1-6.4 and 10.7) the student should be able to:

1.         Write the equation of a circle from center and radius.

2.         Determine the center and radius of a circle from its equation.

3.         Graph a circle using center and radius.

4.         Write the equation of a parabola from vertex, focus, and directrix.

5.         Determine the vertex, focus, and directrix of a parabola from its equation.

6.         Graph a parabola using vertex, focus, and directrix.

7.         Write the equation of ellipse from center, foci, and vertices.

8.         Determine the center, foci and vertices of an ellipse from its equation.

9.         Graph an ellipse using center, foci, and vertices.

10.     Write the equation of a hyperbola from center, vertices, foci, and asymptotes.

11.     Graph a hyperbola from center, vertices, foci, and asymptotes.

12.     Solve applications involving conic sections.

13.     Determine the type of graph for a conic section by transforming the equation.

14.     Graph parametric equations (including trigonometric equations) by hand or using a graphing utility.

15.     Find a rectangular form for a curve defined parametrically, and vice versa.

 Unit VI: Sequences and Series

 Upon completion of this unit (11.1-11.3) the student should be able to:

1.         List the first several terms of finite and infinite sequences.

2.         Use summation notation to express a sum.

3.         Use summation properties to find the sum of a series.

4.         Determine if a sequence is arithmetic.

5.         Find a formula for the n^th term for an arithmetic sequence.

6.         Evaluate the sum of the first n terms of an arithmetic sequence.

7.         Determine if a sequence is geometric.

8.         Find a formula for the n^th term for a geometric sequence, and find its sum.

9.         Evaluate the sum of the first n terms of a geometric sequence.

10.     Find the sum of the terms of an infinite geometric sequence.

 Grade Calculation Method:   The exact method of calculating your grade will be distributed by your instructor at the beginning of the course, based on these guidelines:

                             5 Unit Tests                                         70-85%

                             Cumulative Final Exam                  15-20%

                             Other                                                    0-15%

                             Total                                                       100%

Prepared by: Robin Pepper               Date written or revised: October 30, 2006