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Intermediate Algebra

Geometry

1. Rectangular coordinates, angles and circular/radian measure;
2. Definitions of the six trigonometric functions according to the right triangle, the unit circle, and the rectangular coordinate system;
3. Applications of the right triangle;
4. Simplification of trigonometric expressions;
5. Proofs of trigonometric identities;
6. Graphs of trigonometric functions: period, amplitude, phase shift, asymptotes;
7. Inverse trigonometric functions and their graphs;
8. Trigonometric equations;
9. Solving Triangles: Law of Sines and Law of Cosines;
10. Polar coordinates and equations; and
11. DeMoivre’s Theorem and applications
12. Introduction to vectors.

Upon successful completion of the course, students will be able to:

1. Identify special triangles and their related angle and side measures;
2. Evaluate the trigonometric function of an angle in degree and radian measure;
3. Manipulate and simplify a trigonometric expression;
4. Solve trigonometric equations, triangles, and applications;
5. Graph the basic trigonometric functions and apply changes in period, phase and amplitude to generate new graphs;
6. Evaluate and graph inverse trigonometric functions;
7. Prove trigonometric identities;
8. Convert between polar and rectangular coordinates and equations;
9. Graph polar equations;
10. Calculate powers and roots of complex numbers using DeMoivre’s Theorem; and
11. 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.