Course Syllabus

Course Description:

[INSTRUCTORS: We have included a general description here as a place holder. As with all sections, feel free to keep this information, replace it with your local course description, or remove this section entirely.]

This is a full trigonometry course with algebra concepts reviewed, extended, and integrated when they are relevant to the trigonometric concepts. The trigonometric topics include right triangle trigonometry, unit circle trigonometry, graphs of trigonometric functions, proofs of trigonometric identities, solving trigonometric equations, applications of trigonometric functions (laws of sines and cosines), inverse trigonometric functions, the polar coordinate system, and vectors. The algebra topics include translations and stretches of graphs, graphs of polynomial and rational functions, domain and range, even and odd functions, inverse functions, simplifying and factoring expressions, and equation solving.

Student Learning Outcomes:

[INSTRUCTORS: We have included general student learning outcomes here as a place holder. As with all sections, feel free to keep this information, replace it with your local Student Learning Outcomes, or remove this section entirely.]

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

• apply trigonometric functions to the angles of a right triangle and arcs on the unit circle.
• evaluate trigonometric functions of common angles (using both radian and degree measure) and inverse trigonometric functions.
• recognize, apply, and prove trigonometric identities and solve trigonometric equations.
• create and analyze graphs of polynomial functions, rational functions, trigonometric functions, inverse trigonometric functions, curves in parametric form, and curves in polar form. (Trigonometric function graphing will include changes in period, phase, and amplitude.)
• convert between polar and rectangular coordinates and equations, compute and solve equations involving complex numbers in standard and trigonometric form, and use DeMoivre's Theorem to evaluate powers and roots of complex numbers.
• apply trigonometric and algebraic concepts as problem-solving tools by modeling problems with appropriate equations, including use of the Laws of Sines and Cosines and vector applications with vectors represented in both (a, b) and ai+bj form.

Course Content:

[INSTRUCTORS: Insert course content.]

• Review of geometry: parallel lines and transversals, Pythagorean Theorem, 30-60-90 and isosceles right triangles, triangle congruence postulates, parallelograms, circles and arcs
• Function topics and algebraic techniques: review and extend domain, range, even/odd functions, inverses (use polynomial, rational, root, exponential, logarithmic, and conic sections as examples); factoring, simplifying rational and complex rational expressions involving polynomial and trigonometric expressions (can be done after trigonometric functions are introduced and before working with trigonometric identities and equations); solving equations that are linear, quadratic, quadratic in form, power, radical, rational, and those having complex solutions
• Graphing algebraic functions: review basic graphs (y=x^2, y=x^3, square root, cube root, y=1/x, absolute value) along with their translations and stretches, graphs of piece-wise functions, polynomial functions, and rational functions (include vertical and horizontal asymptotes, but not oblique asymptotes or holes)
• Right triangle trigonometry: angle measure in degrees, minutes, and seconds, definition of the trigonometric functions, coterminal and reference angles, memorization of values of the trigonometric functions for special angles (30, 45, 60, etc), and scientific calculator usage
• Circular functions: definitions of the unit circle and circular functions, reference arcs, development of formulas for arc length and area of a sector, and applications regarding rotations and linear and angular velocity; the student should be at ease with both right triangle trigonometry and circular function developments of trigonometric concepts, regardless of the order in which they are presented (a major emphasis should be placed on the memorization of the exact values of certain right triangles and circular functions)
• Graphing trigonometric functions: the six basic trigonometric graphs (including phase shifts, vertical shifts and changes in period length and amplitude), including domain, range, asymptotes, periods, intercepts, application problems involving modeling and interpretation of intercepts and maximum and minimum values of graphs
• Equations: solve trigonometric equations in radians and in degrees (exact and approximate solutions, solutions on an interval and all solutions), applications of law of sines and cosines
• Inverse functions: inverse trigonometric relations and their graphs for sine, cosine and tangent (with emphasis on the domains and ranges of these functions), using inverse trigonometric functions to solve equations and extension of algebraic inverse functions
• Basic identities: reciprocal identities, Pythagorean identities, cofunction identities, sum and difference of angles, double-angle, half-angle, and the sum and product identities (identities should be memorized with the possible exception of the sum and product identities)
• Vectors: vectors in 2-dimensions (algebraic and geometric) including applications involving force, equilibrium, and work; dot product with applications
• Coordinate systems: converting points and equations from polar coordinates to rectangular coordinates (and the reverse), applications and graphing in the polar coordinate system, parametric equations, graphing parametric equations, trigonometric form of complex numbers, DeMoivre's Theorem and applications, and graphing complex numbers

Textbook:

Great news: your textbook for this class is available for free online!
Algebra and Trigonometry from OpenStax, ISBN 1-947172-10-7

You have several options to obtain this book:

• View online (Links to an external site.) (Links to an external site.)
• Download a PDF (Links to an external site.) (Links to an external site.)
• Order a print copy (Links to an external site.) (Links to an external site.) 

You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.

Important Notes:

• All first week assignments need to be completed and submitted by the due date to avoid possibly being dropped from the class.

• Any student needing accommodations should inform the instructor. Students with disabilities who may need accommodations for this class are encouraged to notify the instructor and contact the Disability Resource Center (DRC) [link to your college's DSPS website] early in the quarter so that reasonable accommodations may be implemented as soon as possible. Students may contact the DRC by visiting the Center (located in room A205) or by phone (541-4660 ext. 249 voice or 542-1870 TTY for deaf students). All information will remain confidential.
• Academic dishonesty and plagiarism will result in a failing grade on the assignment. Using someone else's ideas or phrasing and representing those ideas or phrasing as our own, either on purpose or through carelessness, is a serious offense known as plagiarism. "Ideas or phrasing" includes written or spoken material, from whole papers and paragraphs to sentences, and, indeed, phrases but it also includes statistics, lab results, art work, etc.  Please see the YourCollegeName handbook for policies regarding plagiarism, harassment, etc. [link to your college's academic honesty policies]