Chapter 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant Learning Target: Learning Target: I can generate the graphs for tangent, cotangent, secant, and cosecant.

Tangent Function f(x) = tan (x) D: all real numbers except odd multiples of П/2 R: all real numbers Continuous Increasing on each interval in the domain Symmetric with respect to the origin (odd) Not Bounded No extrema No horizontal asymptotes Vertical asymptotes: x = k(П/2) for all odd integers k End behavior DNE (hence no horizontal asymptotes)

Take a look at the graph of tangent. Why do the vertical asymptotes occur where they do?

Take a look at the graph of cotangent. Why do the vertical asymptotes occur where they do?

Take a look at the graph of Secant. Why do the vertical asymptotes occur where they do?

Take a look at the graph of Cosecant. Why do the vertical asymptotes occur where they do?

Homework Pg. 401 # 3 – 39 every 3 rd