This lesson gives students an opportunity to study the graphs of three additional trigonometric functions: secant, cosecant, and cotangent. Students begin by connecting the geometric representation of the trigonometric ratios to the new functions, as they make sense of the new functions (MP1). Then students use the ratio definitions and reciprocal identity definitions to create graphs of each function. As students compare the graphs of the more familiar sine, cosine, and tangent functions with the new graphs of the secant, cosecant, and cotangent functions, they leverage the structure of the reciprocal identities to identify important points and asymptotes (MP7).

Note that while there are some applications of these trigonometric functions in engineering and robotics, they are mostly useful as an abbreviation for their reciprocal functions.