Mastering the Graphs of Reciprocal Trig Functions

Miacademy & MiaPrep Learning Channel

This comprehensive Precalculus lesson guides students through the process of graphing the three reciprocal trigonometric functions: cosecant (csc), secant (sec), and cotangent (cot). By building upon prior knowledge of sine, cosine, and tangent graphs, the video demonstrates how to use these familiar functions as guides to construct new graphs. It explicitly details how to identify vertical asymptotes where the original functions equal zero and explains the behavior of the curves as they approach these undefined points. The video covers key mathematical themes including periodic functions, domain and range expressed in set notation, and the effects of transformations such as vertical stretches, horizontal compressions, and phase shifts. It systematically breaks down the properties of each function, clarifying why reciprocal functions lack amplitude and how their periods are calculated. The lesson progresses from parent functions to more complex examples involving transformations, requiring students to recalculate asymptote locations and key points. Ideally suited for high school trigonometry or precalculus classrooms, this video serves as both a direct instruction tool and an interactive study guide. It includes built-in pause points that prompt students to complete tables of values, sketch graphs on guided notes, and predict transformations before seeing the solution. This interactive format encourages active participation and helps educators identify student misconceptions regarding asymptotic behavior and graph transformations.