10/20/2019 10:21:15 PM | MATH 58 Course Outline as of Summer 2019
| Changed Course |

CATALOG INFORMATION |
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Discipline and Nbr: MATH 58 | Title: PRECALCULUS TRIGONOMETRY | |

Full Title: Precalculus Trigonometry | ||

Last Reviewed:10/22/2018 |

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 |

Grading: Grade Only

Repeatability: 00 - Two Repeats if Grade was D, F, NC, or NP

Also Listed As:

Formerly:

**Catalog Description:**

Trigonometry topics, including trigonometric identities, equations, functions, inverse functions, and graphs, polar coordinates, parametric equations, complex numbers, vectors and applications.

**Prerequisites/Corequisites:**

Completion of MATH 156 or MATH 154 or MATH 155 or appropriate placement based on AB 705 mandates

**Recommended Preparation:**

**Limits on Enrollment:**

**Schedule of Classes Information**

Description:

Trigonometry topics, including trigonometric identities, equations, functions, inverse functions, and graphs, polar coordinates, parametric equations, complex numbers, vectors and applications.

(Grade Only)

Prerequisites:Completion of MATH 156 or MATH 154 or MATH 155 or appropriate placement based on AB 705 mandates

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: | B MC | Communication and Analytical Thinking Math Competency |
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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__**Student Learning Outcomes:**

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

1. Define and graph the six trigonometric functions and their inverses, solve equations involving

trigonometric functions symbolically and graphically, and verify trigonometric identities.

2. Use trigonometric functions, identities, and Laws of Sines and Cosines to solve application

problems.

3. Define, graph, and demonstrate appropriate applications of vectors, complex numbers in

trigonometric form, polar coordinates, and parametric equations.

**Objectives:**

During this course, students will:

1. Define and apply the trigonometric functions, using right triangle and unit circle approaches,

and using degree and radian measures.

2. Verify and apply trigonometric identities.

3. Solve equations involving trigonometric functions both graphically and analytically.

4. Graph trigonometric functions and their transformations.

5. Define and graph the inverse trigonometric functions.

6. Solve applications and modeling problems using the trigonometric functions, identities, and

the Laws of Sines and Cosines.

7. Represent complex numbers in trigonometric form and perform operations.

8. Use vectors to model applications in mathematics and science.

**Topics and Scope**

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

B. Reflections

C. Period

D. Phase (horizontal) shift

E. Vertical shifts

IV. Inverse Functions

A. Definitions

B. Properties

C. 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:**

1. Reading outside of class (0-60 pages per week)

2. Problem sets (1-8 per week)

3. Quizzes (0-4 per week)

4. Projects (0-10)

5. Exams (2-6)

6. Final exam

**Methods of Evaluation/Basis of Grade.**

Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing. | Writing 0 - 0% |
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None | |||

This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course. | |||

Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills. | Problem Solving 5 - 20% |
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Problem sets | |||

Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams. | Skill Demonstrations 0 - 0% |
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None | |||

Exams: All forms of formal testing, other than skill performance exams. | Exams 70 - 95% |
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Exams and quizzes | |||

Other: Includes any assessment tools that do not logically fit into the above categories. | Other Category 0 - 10% |
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Projects |

**Representative Textbooks and Materials:**

Precalculus: Mathematics for Calculus. 7th ed. Stewart, James and Redlin, Lothar and Watson, Saleem. Cengage L. 2015

Precalculus. 3rd corrected ed. Stitz, Carl and Zeager, Jeffrey. Open Source Text. 2013 (classic)