Ep 3. Review - Functions and Trigonometry

Understanding Calculus: Problems, Solutions, and Tips season 1 episode 3 is titled "Review - Functions and Trigonometry." The episode serves as a thorough review of all the functions and trigonometry covered in previous episodes, with a focus on the most common trouble areas for calculus students.

The episode begins with a brief overview of functions and how they are represented using notation. From there, the show breaks down some of the most important properties of functions, such as their domain and range, increasing and decreasing intervals, and points of continuity. The host provides clear examples and tips for how to identify these properties for any given function, along with some common pitfalls to avoid.

Next, the show dives into trigonometry, starting with a review of the basic trig functions (sine, cosine, and tangent) and their graphs. The host emphasizes the importance of understanding these functions at a deep level, since they are among the most common functions used in calculus. She also touches on some of the more advanced trigonometric functions, such as secant, cosecant, and cotangent.

Throughout the episode, the host provides plenty of helpful tips and tricks for mastering functions and trigonometry. For example, she discusses some of the most common mistakes students make when dealing with asymptotes or inverse functions, and offers strategies for avoiding these errors. She also provides a helpful mnemonic device for remembering the signs of trig functions in each of the four quadrants.

One of the highlights of the episode is a series of practice problems designed to test students' knowledge of functions and trigonometry. The problems range in difficulty from basic to advanced, and cover a variety of topics, including finding limits, solving equations, and graphing functions. The host provides step-by-step solutions to each problem, pointing out common mistakes and offering hints for solving similar problems in the future.

Overall, "Review - Functions and Trigonometry" is an excellent resource for anyone looking to solidify their understanding of these fundamental concepts. Whether you're a calculus student struggling to keep up with the material or a self-directed learner looking for a comprehensive review, this episode has plenty to offer. With its clear explanations, helpful examples, and challenging practice problems, it will help you build a strong foundation for the rest of your calculus studies.