Description:

This is a course in trigonometric functions and graphs. Emphasis will be on understanding function notation, definitions, algebraic relations, real-world applications, graphing in the real and complex plane, inverse functions, polar functions and vectors. Students who take Math 172 and Math 173 will receive at most five hours of credit toward graduation. 3 hrs./wk.

Associated Costs: These are additional (out-of-pocket) expense considerations that students should expect in addition to the course tuition, fees, and textbooks. $0 to $100.

Supplies: Refer to the instructor’s course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

Course Objectives:

Upon successful completion of this course the student should be able to:

1. Apply trigonometric functions to real-world situations.
2. Verify trigonometric identities.
3. Solve trigonometric equations.
4. Solve and find area of triangles using trigonometric formulas.
5. Analyze the graphs of trigonometric, inverse trigonometric, and polar functions.
6. Calculate products, quotients, powers, and roots of complex numbers in trigonometric form.

Content Outline & Competencies:

I. The Six Trigonometric Functions
   A. Determine the six trigonometric functions of an angle in standard
position given a  point on its terminal side.
   B. Determine the remaining trigonometric functions of an angle given
the value of one trigonometric function and the quadrant in which the
angle lies.
   C. Determine the six trigonometric functions of an angle in a triangle
given two sides.
   D. Calculate the six trigonometric functions of an angle using a
calculator.
   E. Determine exact values of the six trigonometric functionsgiven a
30°, 45°, 60°, or quadrantal angle.
   F. Determine the six trigonometric functions of an angle in standard
position using reference angles.

II. Applications
   A. Solve real world-problems involving angles of elevation and
depression.
   B. Calculate the length of an arc and the area of a sector in a
circle.

III.  Graphs of Trigonometric Functions
   A. Graph the six basic trigonometric functions of the form y = k +
Afunc(Bx + C).
   B. Determine the equation of a function given its graph.
   C. Graph combinations of functions.

IV. Trigonometric Identities
   A. Simplify trigonometric expressions using trigonometric identities.
   B. Prove trigonometric identities.
   C. Evaluate function values using sum, difference, double, and half
angles identities.
 
V. Inverse Trigonometric Functions
   A. Evaluate inverse trigonometric functions with and without a
calculator.
   B. Evaluate expressions involving inverse trigonometric functions.
 
VI. Trigonometric Equations
   A. Solve trigonometric equations on a given interval in degrees or
radians.
   B. Solve trigonometric equations for all angle solutions.

VII. Triangles
   A. Solve triangles using trigonometric ratios, the Law of Sines, or the
Law of Cosines, where appropriate.
   B. Find areas of triangles.
   C Apply the solutions of triangles to real-world problems.

VIII. Vectors
   A. Determine the magnitude and direction of vectors. 
   B. Resolve vectors into components.
   C. Find the sum, difference, dot product, magnitude, and angle between
two vectors in algebraic form.
   D. Apply vectors to real-world problems.

IX. Complex Numbers
   A. Graph in the complex plane.
   B. Convert complex numbers from standard form to trigonometric form and
vice versa.
   C. Find products, quotients, powers, and roots of complex numbers.

X. Polar Coordinates
   A. Convert from rectangular to polar coordinates and vice versa.
   B. Convert equations from rectangular to polar form and vice versa.
   C. Graph polar equations.

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

 Unit Exams, Unit Papers and/or Unit Projects  40% - 80%
 Homework, Quizzes and/or Small Projects        0% - 50%
 Final Exam**                                  10% - 40%

**The final exam must count at least as much as any unit exam, unit paper
or unit project.  In any course where unit exams are not proctored, the
instructor may require that the student score at least a 70% on the final
exam to earn a ‘C’ for the course.  At the instructor's discretion, the
grade on all or any part of the final exam may replace any lower test
score.

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level math course on a space available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.