Precalculus II: Trigonometry

Course Number:

MTH 112Z

Transcript Title:

Precalculus II: Trigonometry

Created:

Aug 15, 2022

Updated:

Apr 28, 2023

Total Credits:

4

Lecture Hours:

30

Lecture / Lab Hours:

20

Lab Hours:

0

Satisfies Cultural Literacy requirement:

No

Satisfies General Education requirement:

Yes

Grading Options

A-F, P/NP, Audit

Default Grading Options

A-F

Repeats available for credit:

0

Alignment with Institutional Learning Outcomes

Major

1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)

Not Addressed

4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)

Minor

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Institutional Learning Outcomes (ILOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Suggested Outcome Assessment Strategies

The determination of assessment strategies is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: writings (journals, self-reflections, pre writing exercises, essays), quizzes, tests, midterm and final exams, group projects, presentations (in person, videos, etc), self-assessments, experimentations, lab reports, peer critiques, responses (to texts, podcasts, videos, films, etc), student generated questions, Escape Room, interviews, and/or portfolios.

Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

Course Content

Outcome #1: Translate among various systems of measure for angles including radians, degrees, and revolutions.

• Graphing
• Reference angles
• Unit circles

Outcome #2: Represent, manipulate, and evaluate trigonometric expressions in terms of sides of a right triangle and in terms of coordinates of a unit circle.

• Unit circles
• Angles
• Circles, Triangles, Sine and Cosine
• The other Trigonometric Functions
• Reference Angles

Outcome #3: Graph, transform, and analyze trigonometric functions using amplitude, shifts, symmetry, and periodicity.

• Unit Circles
• Sinusoidal Graphs
• Period, Amplitude, Symmetry
• Graphs of Other Trig Functions
• Period, Symmetry
• Modeling

Outcome #4: Manipulate trigonometric expressions and prove trigonometric identities.

• Circles, Triangles, Sine and Cosine
• Other Trigonometric Functions
• Trig Identities

Outcome #5: Solve trigonometric equations using inverses, periodicity, and identities.

• Circles, Triangles, Sine and Cosine
• Other Trigonometric Functions
• Trig Identities

Outcome #6: Define, represent, and operate with vectors both geometrically and algebraically.

• Polar Coordinates
• Parametric Equations
• Vectors and Their Applications

Outcome #7: Apply the law of sines and the law of cosines to determine lengths and angles.

• Circles, Triangles, Sine and Cosine
• Non-right triangles: Law of Sines and Cosines
• Modeling

Outcome #8: Use variables, trigonometric functions, and vectors to represent quantities, create models, find solutions, and communicate and interpretation of the results.

• Unit Circles
• Sinusoidal Graphs
• Modeling
• Vectors and Their Applications
• Law of Sines and Cosines
• Parametric equations

Outcome #9: Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

• Unit Circles
• Sinusoidal Graphs
• Modeling
• Vectors and Their Applications
• Law of Sines and Cosines
• Polar Coordinates and Complex Numbers
• Parametric Equations

Suggested Texts and Materials

• Lippman, D.  & Rasmussen,M. Precalculus 1: An Investigation of Functions, Edition 2.2. The text is open source and available online at: https://www.opentextbookstore.com/precalc/2.2/Precalc1.pdfPDF
• Graphing calculator or graphing app such as Desmos - required

Department Notes

Answers to all application problems will be given in complete sentences with correct units. The grade will include at least one project.