December 15, 2012
The study of trigonometric functions, their inverses and their graphs, identities and proofs related to trigonometric expressions, trigonometric equations, solving right triangles, solving triangles using the Law of Cosines and the Law of Sines, polar coordinates, and introduction to vectors.
- Rectangular coordinates, angles and circular/radian measure;
- Definitions of the six trigonometric functions according to the right triangle, the unit circle, and the rectangular coordinate system;
- Applications of the right triangle;
- Simplification of trigonometric expressions;
- Proofs of trigonometric identities;
- Graphs of trigonometric functions: period, amplitude, phase shift, asymptotes;
- Inverse trigonometric functions and their graphs;
- Trigonometric equations;
- Solving Triangles: Law of Sines and Law of Cosines;
- Polar coordinates and equations; and
- DeMoivre’s Theorem and applications
- Introduction to vectors.
Upon successful completion of the course, students will be able to:
- Identify special triangles and their related angle and side measures;
- Evaluate the trigonometric function of an angle in degree and radian measure;
- Manipulate and simplify a trigonometric expression;
- Solve trigonometric equations, triangles, and applications;
- Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs;
- Evaluate and graph inverse trigonometric functions;
- Prove trigonometric identities;
- Convert between polar and rectangular coordinates and equations;
- Graph polar equations;
- Calculate powers and roots of complex numbers using DeMoivre’s Theorem; and
- Represent a vector (a quantity with magnitude and direction) in the form <a,b> and ai+bj.
Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.
A college level text designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.
Course does not transfer to UC’s