NORTHWEST-SHOALS
COMMUNITY COLLEGE
TITLE OF
COURSE: Pre-Calculus Trigonometry (MTH 113)
DIVISION: Mathematics,
Science, and Technology
COURSE DESCRIPTION: This course
includes the study of trigonometric (circular functions) and inverse
trigonometric functions, and includes extensive work with trigonometric
identities and trigonometric equations. The course also covers vectors, complex
numbers, DeMoivre's Theorem, and polar coordinates. Additional topics may
include conic sections, sequences, and using matrices to solve linear systems.
HOURS: Credit: 3 Contact:
3 Lecture: 3 Clinical: 0 Lab:
0
PREREQUISITE(S): All core
mathematics courses in Alabama must have as a minimum prerequisite high school
Algebra I, Geometry, and Algebra II with an appropriate mathematics placement
score. An alternative to this is that the student should successfully pass with
C or higher (S if taken as pass/fail) Pre-Calculus Algebra, MTH 112.
COREQUISITE(S): None
REQUIRED
TEXTBOOK(S): Precalculus; 7th Edition; R. E. Larson and R. P. Hostetler with
David C. Falvo, Houghton-Mifflin, 2007.
SUPPLIES: Scientific or
graphing calculator is highly recommended.
GENERAL
EDUCATION OBJECTIVE: All associate degree graduates should be able to use
the mathematical concepts, notations, and manipulations needed in their field
of study or occupation. (3)
COURSE
OBJECTIVE(S): Upon successfully completing Pre-Calculus Trigonometry,
MTH 113, the student should be able to:
1.
Graph
an angle in standard position; evaluate the six trigonometric functions for a
given angle.
2.
Convert
between radian and degree measure.
3.
Recall
the six basic trigonometric functions for the common angles.
4.
Solve
right triangles.
5.
Solve
triangles using the Law of Cosines and the Law of Sines.
6.
Recall
the fundamental trigonometric identities and apply these to prove other
identities or to solve trigonometric equations.
7.
Evaluate
and graph the six basic trigonometric functions and their inverses.
8.
Write
the trigonometric form of a complex number; represent complex numbers
graphically; perform operations with these complex numbers (including multiply,
divide, and find roots); apply DeMoivre’s Theorem.
9.
Use
polar coordinates and graph polar equations.
10. Perform the basic operations on vectors in
a plane; find the dot product
of two vectors; use vectors to solve related
applications.
A comprehensive
final exam will be given and counted toward the student’s final average. Make-up examinations, as such, will not
generally be given.
OUTLINE
OF COURSE TOPICS:
I. Trigonometry
A.
Angles: Radian and Degree Measure
B.
Trigonometric Functions: The Unit
Circle
C.
Right Triangle Trigonometry
D.
Trigonometric Functions of Any Angle
E.
Graphs
of Sine and Cosine Functions
F.
Graphs
of Other Trigonometric Functions
G.
Inverse Trigonometric Functions
H.
Applications and Models
II. Analytic Trigonometry
A.
Using Fundamental Identities
B.
Verifying Trigonometric Identities
C.
Solving Trigonometric Equations
D.
Sum and Difference Formulas
E.
Multiple-Angle Formulas and Product-to-Sum Formulas
F. Inverse Trigonometric Functions
III.
Additional Topics in
Trigonometry
A.
Law of Sines
B.
Law of
Cosines
C.
Vectors
in the Plane
D.
Vectors
and Dot Products
E.
Trigonometric
Form of A Complex Number
F.
De
Moivre’s Theorem and nth Roots of
Complex Numbers
IV.
Topics
from Analytic Geometry
A. (Optional)
Plane Curves and Parametric Equations
B. (Required)
Polar Coordinates
C. (Optional)
Polar Equations of Conics
AMERICANS WITH DISABILITIES
ACT POLICY: It is the policy of Northwest-Shoals
Community College to comply with the Americans with Disabilities (ADA) Act. Any
student covered under this act needing and desiring reasonable accommodations
for this class should notify Linda Waide at 331-5321. See NWSCC catalog for
additional details.
ATTENDANCE POLICY:
Because class attendance is considered to be essential to the accomplishment of
course objectives, excessive absences are discouraged. At no time should a
student miss more than 20% of the class meetings for a course. These absences
also include any absences accrued during late registration. Failure to adhere
to the 20% policy may result in a failing grade based on academic performance.
Students should discuss with the instructor what is considered “excessive” for
a particular course. Any variation of this policy must be approved through the
Chief Instructional Officer. A student who is absent due to required
participation in a school activity must be allowed to make up work, according
to guidelines issued by individual instructors.
WITHDRAWAL POLICY: A student who is unable to complete a course
is expected to withdraw from that course by the end of 60% of class
meetings. A student who withdraws by the
date published in the schedule will receive a grade of “W” for the course. This
withdrawal is done only by student request.
The grade of “W” is allowed regardless of
the student’s grades to the point of withdrawal.
After the designated date of class withdrawal, the approval
of the Chief Instructional Officer is required prior to allowing a student to
withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal
failing) will be made by the instructor for the course and is based on the
student’s grades to the point of withdrawal.