Precalculus: Periodic Functions from Coursera

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Syllabus

Module 1: Periodic Functions

In this course, we expand our collection of functions which we can use to model by studying periodic functions. Periodic functions are functions whose graphs repeat themselves after a certain point. It is natural to study periodic functions as many natural phenomena are repetitive or cyclical: the motion of the planets in our solar system, days of the week, seasons, and the natural rhythm of the heart. Thus, the functions introduced in this course add considerably to our ability to model physical processes. In this module, we begin by learning methods of measuring angles.

Module 2: Right Triangle Trigonometry

Many common phenomena have oscillatory or periodic behavior. To model this behavior requires an understanding of functions that exhibit periodic behavior like sine, cosine, and tangent. These functions are introduced using right triangles in this module, which then lets us explore their algebraic relations.

Module 3: Sine and Cosine as Periodic Functions

Sine and cosine are now introduced using the unit circle, which is the circle centered at the origin with radius one. This definition of our key periodic functions extends the definition originally introduced with right triangles.

Module 4: The Tangent and Other Periodic Functions

The most basic periodic functions, sine and cosine, were defined for all real numbers. We now study their quotients and reciprocals. However, care must be taken to ensure we do not divide by zero. In this module, we will complete our catalog of periodic functions

Module 5: (Some) Identities of Periodic Functions

In an effort to simplify the work involving our periodic functions, we introduce common identities. This dramatically increases their usefulness in applications. This module will emphasize the development of a small core of identities that are continually needed and can be used to determine a much larger collection. While the number of identities is small in this module, an understanding of these and how to derive others from them is essential for success as you continue your studies.

Good to know

Know what's good

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Develops the mathematical skills needed for science and computer science, which are in high demand in the job market

Uses real-life data and examples to make the material relevant and engaging

Suitable for students with diverse backgrounds and interests in science, math, or technology

Provides a solid foundation for students who plan to pursue further studies in mathematics or related fields

Covers a range of topics, including functions, properties, and applications to data analysis

Taught by an experienced instructor with a strong reputation in the field

Reviews summary

Precalculus: well-received trig & periodic functions course

According to students, this course in precalculus covers periodic trigonometric functions and is largely positive. Students found it challenging but learned trigonometric concepts well and say the course is well-designed and well-taught. Instructors provide clear explanations, examples, and stories to help students understand. The course uses video lessons, quizzes, assignments, and discussion forums to facilitate learning. Be aware that some quizes may have errors.

Well-designed course with helpful resources

"Outstanding teacher and well designed online course."

"The course is amazing. It helped me to understand the logic of periodic functions instead only memorize those functions."

"It requires a good mathematical background, and it does not include introductory concepts."

Engaging and knowledgeable instructor

"I enjoyed the course through and through. Joseph is a great instructor."

"TEACHER IS TOO GOOD"

"Thank you very much for your teaching, Sir! Your lectures are always clean and clear."

Clear explanations and examples

"The explanations are very clear"

"Extremely well taught! Superb explanations and examples."

"The course is challenging. I learned a lot about trigonometric functions and their behavior."

Occasional errors in quizzes

"some quizes had some errors"

"I felt there was a gap between what was taught and what was tested."

"I think a couple of the test/quiz questions were not fairly graded."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Precalculus: Periodic Functions with these activities:

Identify potential mentors in the field of mathematics

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Build connections with experienced professionals who can provide guidance, support, and encouragement throughout your learning journey.

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Attend conferences and workshops
Reach out to professors and industry experts
Join professional organizations
Explore online platforms
Ask for recommendations from peers

Volunteer at a local math museum or science center

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Connect with others who share your interest in mathematics, gain practical experience, and make a meaningful contribution to your community.

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Research local math museums or science centers
Contact the organization to inquire about volunteer opportunities
Complete the application process
Attend training and orientation
Fulfill your volunteer duties

Gather a collection of resources on trigonometric functions

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Organize and expand your knowledge of trigonometric functions by compiling a comprehensive collection of resources.

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Identify different types of resources
Search for books, articles, videos, and websites
Organize the resources into categories
Annotate the resources with brief descriptions
Share the collection with others

Four other activities

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Solve problems involving periodic functions

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Sharpen your problem-solving skills and deepen your understanding of periodic functions by working through practice problems.

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Review the concepts of periodic functions
Gather practice problems from the textbook or online resources
Solve the problems using appropriate methods
Check your answers and identify areas for improvement
Repeat until you are confident in solving a variety of problems

Design a lesson plan on periodic functions

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Develop your teaching skills and deepen your understanding of periodic functions by creating a comprehensive lesson plan.

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Review the concepts of periodic functions
Identify the learning objectives for the lesson
Choose appropriate activities and materials
Develop a detailed lesson plan
Share your lesson plan with others for feedback

Create a visual representation of a periodic function

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Reinforce your understanding of periodic functions by visualizing them in a creative and engaging way.

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Choose a periodic function to represent
Determine the amplitude, period, and phase shift of the function
Create a visual representation using graphing software or other tools
Label the key features of the graph
Write a brief explanation of how the graph represents the function

Tutor fellow students in precalculus functions

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Enhance your own understanding and build confidence by helping others master the concepts of precalculus functions.

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Offer your services as a tutor
Identify students who need help
Prepare lesson plans or materials
Meet with students regularly to provide guidance and support
Evaluate students' progress and provide feedback

Career center

Learners who complete Precalculus: Periodic Functions will develop knowledge and skills that may be useful to these careers:

Data Analyst

As a Data Analyst, your work revolves around studying and interpreting data, helping turn raw data into meaningful insights to help businesses make more informed decisions. Your knowledge of periodic functions aids in analyzing cyclical data to find trends and patterns. This course will also provide a foundation for calculus, later assisting you in more complex data analysis using the principles of calculus and periodic functions together.

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Actuary

Actuaries are professionals who use mathematical and statistical techniques to quantify and manage risk. In this role, employers seek candidates with strong analytical and problem-solving skills, for which this course builds a foundation. Additionally, a portion of actuarial work involves the analysis of financial data, a field where periodic functions are used to analyze and forecast repetitive or cyclical trends in financial markets.

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Operations Research Analyst

Operations Research Analysts design and analyze mathematical models to help businesses make better decisions about resource allocation, scheduling, and more. This course provides an introduction to the mathematical tools and techniques used extensively by Operations Research Analysts and can help you develop foundational skills to move into this field.

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Financial Analyst

Financial Analysts use complex modeling techniques and periodic functions to analyze and forecast market performance, analyze companies, and make sound investment decisions. This course can help you begin building the skills to make data-driven recommendations and support financial decisions.

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Software Engineer

Software Engineers are in high demand and design, develop, and maintain software applications. This course can be an asset to Software Engineers in many different industries who may need to analyze and model cyclical data.

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Biostatistician

Biostatisticians use statistics for the analysis and interpretation of biological data. This course can be helpful in building a foundation for further study in the field of biostatistics.

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Market Researcher

Market Researchers study and interpret market data to help businesses make decisions. Periodic functions are often used in market research to analyze seasonal trends and patterns.

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Epidemiologist

Epidemiologists study the causes of disease and other health problems in populations. They use statistical techniques to analyze data and identify trends. This course can help Epidemiologists build a foundation for using periodic functions to analyze cyclical data, such as the spread of diseases.

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Meteorologist

Meteorologists study the atmosphere and its interactions with the Earth's surface. Periodic functions are often used to model weather patterns and forecast weather conditions.

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Civil Engineer

Civil Engineers design and build infrastructure projects, such as roads, bridges, and buildings. Periodic functions can be used to analyze and model the behavior of these structures under different conditions.

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Mechanical Engineer

Mechanical Engineers design and build machines and other mechanical devices. Periodic functions can be used to analyze and model the behavior of these machines under different conditions.

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Electrical Engineer

Electrical Engineers design and build electrical systems. Periodic functions can be used to analyze and model the behavior of these systems under different conditions.

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Chemical Engineer

Chemical Engineers design and build chemical plants and other chemical processes. Periodic functions can be used to analyze and model the behavior of these processes under different conditions.

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Nuclear Engineer

Nuclear Engineers design and build nuclear power plants. Periodic functions can be used to analyze and model the behavior of these plants under different conditions.

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Petroleum Engineer

Petroleum Engineers design and build systems to extract oil and gas from the Earth. Periodic functions can be used to analyze and model the behavior of these systems under different conditions.

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