Mastering the Graph of the Tangent Function

Miacademy & MiaPrep Learning Channel

This detailed mathematics video provides a comprehensive guide to understanding and graphing the tangent function, a fundamental concept in trigonometry and precalculus. It begins by defining tangent as the ratio of sine to cosine and visually exploring the resulting characteristics, such as its periodic nature, vertical asymptotes, and lack of amplitude. By comparing the tangent graph directly to sine and cosine graphs, the video makes abstract properties like domain restrictions and periodicity intuitive and accessible. The video delves deeply into transformations, explaining how to modify the parent function using the standard transformation formula. It covers vertical and horizontal stretches and compressions, as well as vertical and phase shifts. Through step-by-step worked examples, viewers learn how to graph complex tangent functions and, conversely, how to derive the algebraic equation from a provided graph. The lesson explicitly addresses how parameters affect the graph's shape and position, with a specific focus on calculating the new period and locating asymptotes. Ideally suited for Precalculus, Algebra II, or Trigonometry classrooms, this video serves as both an introduction and a practice tool. It includes built-in pause points that encourage active student participation, allowing them to predict transformations and solve problems before seeing the solution. The clear visual aids and logical progression make it an excellent resource for demystifying one of the more challenging trigonometric graphs for high school students.