UW COLLEGES

                                             DEPARTMENT OF MATHEMATICS

                                                         COURSE GUIDELINES

Course Title:  Trigonometry

Course No.:  MAT 113 No. of Credits:  2

Contact hrs/wk:  2 hrs/wk Lecture/Discussion

Course Prerequisites:  (a) A grade of C or better in MAT 110 or (b) concurrent registration in MAT 110 or (c) placement based on placement test score

Catalog description:

Trigonometric functions, their basic properties and graphs, identities, inverse trigonometric functions, solving trigonometric equations, solutions of triangles

Course content (list of topics normally covered):

1. Angles and Applications

- Radian measure;

- arc length;

- area of a sector;

- angular velocity

2. Trig Functions-Basic Definitions

- Angles in standard position;

- quadrantal angles;

- circular functions;

- unit circle

3. Right Triangle Trigonometry and Applications

- Trig functions of acute angles, complementary angles, special angles;

- calculator values of trig functions;

-  finding the angles given the trig function;

- Applications: angles of elevation and depression;

- bearing; vectors, navigation;

- inclined planes

4. Trig Functions of Any Angle

- Coterminal angles;

- negative angles;

- reference angles

5. Graphs of Trig Functions

- Periodic phenomena;

- amplitude, period, phase shift of sine, cosine, and tangent functions;

- graphs of reciprocal functions

6. Basic Identities

- Reciprocal, ratio, Pythagorean, negative, cofunction identities;

-  Proving identities

7. Trig Functions of Two Angles

- Addition, Subtraction, double angle, half angle formulas;

- product to sum and sum to product formulas;

- harmonic functions

8. Oblique Triangle Solution and Applications

- Law of Sines;

- Law of Cosines;

- Area Formulas

9. Inverse Trig Functions and Solving Trig Equations

- Definitions and graphs of inverse trig functions;

- basic and complete solutions of trig equations

10. Optional Topics

- Complex Numbers: Polar form; multiplication and division in polar form; De Moivre's Theorem; Roots of Complex Numbers

- Polar Coordinates:  Conversion for rectangular to polar and vice-versa; polar

equations and graphs

Content-based department proficiencies:

• Basic concepts of the circular functions
• Applications of triangle trigonometry
• Use of trig identities
• Understanding of graphs of the trig functions
• Understanding of inverse trig functions

Colleges-wide proficiencies assigned to course:

Students should be able to demonstrate the following:

A. Analytical skills Performance Indicators: Students should be able to:

1. Interpret and synthesize information and ideas.

4. Select and apply scientific and other appropriate methodologies.

B. Quantitative skills Performance Indicators: Students should be able to:

1. Solve quantitative and mathematical problems.

2. Interpret graphs, tables, and diagrams.

Representative textbooks used for the courses:

Trigonometry, 6^th edition, Sullivan, Prentice-Hall

Trigonometry enhanced with Graphing Utilities, 2^nd edition, Sullivan and Sullivan

Trigonometry, 5^th Edition, Larson, Houghton-Mifflin

Approved April 22, 2006