Trigonometry — Graphing Trigonometric Functions

About this lesson

This unit introduces students to the graphical representation and properties of the sine and cosine functions. It begins with guided activities where students complete tables of values, plot points, and draw curves for both functions, then extends the graphs using additive inverses. The properties are then stated: the domain of both sine and cosine is all real numbers, their range is [-1, 1], they are periodic with period 2π, and their maximum and minimum values are 1 and -1, occurring at specific points. A real-world application is presented involving the depth of water in a port modeled by S = 6 sin (15n)° + 10, where students calculate the depth at various times and determine when the depth reaches 10 metres. The unit includes exercises where students find maximum and minimum values and ranges for functions like y = 3 sin x and y = 2 cos x, and complete tables and match rules to graphs.