# SRJC Course Outlines

 12/6/2023 6:25:02 AM MATH 58 Course Outline as of Summer 2011 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 58 Title:  PRECALCULUS TRIGONOMETRY Full Title:  Precalculus Trigonometry Last Reviewed:2/10/2020

 Units Course Hours per Week Nbr of Weeks Course Hours Total Maximum 3.00 Lecture Scheduled 3.00 17.5 max. Lecture Scheduled 52.50 Minimum 3.00 Lab Scheduled 0 6 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 3.00 Contact Total 52.50 Non-contact DHR 0 Non-contact DHR Total 0

 Total Out of Class Hours:  105.00 Total Student Learning Hours: 157.50

Title 5 Category:  AA Degree Applicable
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:

Catalog Description:
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Trigonometric functions and their graphs, trigonometric identities, trigonometric equations, inverse trigonometric functions, complex numbers, polar coordinates, parametric equations, vectors, and applications.

Prerequisites/Corequisites:
Completion of MATH 155 or higher (V1)

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Trigonometric functions and their graphs, trigonometric identities, trigonometric equations, inverse trigonometric functions, complex numbers, polar coordinates, parametric equations, vectors, and applications.

Prerequisites:Completion of MATH 155 or higher (V1)
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

 Associate Degree: Effective: Fall 1981 Inactive: Area: BMC Communication and Analytical ThinkingMath Competency CSU GE: Transfer Area Effective: Inactive: B4 Math/Quantitative Reasoning Fall 2006 B4 Math/Quantitative Reasoning Fall 1981 Fall 1996 IGETC: Transfer Area Effective: Inactive: CSU Transfer: Transferable Effective: Fall 2006 Inactive: UC Transfer: Effective: Inactive: C-ID:

Certificate/Major Applicable: Both Certificate and Major Applicable

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:
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Upon completion of the course, students will be able to:
1.   Define the trigonometric functions, using both right triangle and unit circle.
2.   Use radian measure to find arc length, sector area, and linear and
angular velocity.
3.   Verify trigonometric identities.
4.   Solve, both graphically and analytically, equations involving
trigonometric functions.
5.   Graph trigonometric functions and transformations of these functions.
6.   Define and graph the inverse trigonometric functions.
7.   Apply trigonometric functions and identities to solve applications and
modeling problems.
8.   Solve right and oblique triangles using the trigonometric
functions and the Laws of Sine and Cosine.
9.   Represent complex numbers in, and perform operations using,
trigonometric form.
10. Use vectors to model applications in mathematics and science.

Topics and Scope
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I.    Trigonometric Functions
A. Radian and degree measures of angles
1. Arc length
2. Area of a sector
3. Linear and angular velocity
B. Right triangle and unit circle definitions
C. Characteristics of trigonometric functions
II.   Identities and Conditional Equations
A. Fundamental identities
B. Sum and difference identities
C. Related identities and their derivations
D. Conditional trigonometric equations and applications
III. Graphical Representation of Trigonometric Functions
A. Amplitude and reflections
B. Period
C. Phase (horizontal) shifts
D. Vertical shifts
IV.  Inverse Functions
A. Definitions
B. Properties of inverse functions
C. Inverse trigonometric functions and their graphs
V.   Solutions of Triangles
A. Right triangles
B. Oblique triangles
C. Laws of Sines and Cosines
D. Applications
VI.  Complex Numbers, Polar Coordinates, and Parametric Equations
A. Definitions
B. Operations
C. Graphical representation of complex numbers
D. DeMoivre's Theorem
E. Polar coordinates
F. Parametric equations
VII. Two Dimensional Vectors
A. Geometric and analytic definitions
B. Algebra of vectors
C. Trigonometric form of vectors
D. Dot product
E. Applications

Assignments:
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1.  Daily reading outside of class (20-50 pages per week).
2.  Problem set assignments from required text(s)or supplementary
materials chosen by the instructor (1-6 per week).
3.  Quizzes (0-4 per week).
4.  Exams (3-8 per term).
5.  Projects (for example, computer explorations or modeling activities, 0-10 per term).