Graphs of Trigonometric Functions (Chapter 2.7)

This set of flashcards covers key concepts and characteristics of the tangent, cotangent, cosecant, and secant trigonometric functions as discussed in the lecture.

What are the four trigonometric functions discussed in this lecture segment besides sine and cosine?

Tangent, Cotangent, Cosecant, Secant.

What is the key characteristic of the tangent function's domain?

The tangent function is undefined where cosine equals zero, which occurs at odd multiples of π/2.

What behavior of the tangent function is observed as x approaches π/2?

The y values approach infinity, indicating a vertical asymptote.

What is one period of the tangent function?

The distance between the vertical asymptotes at -π/2 and π/2.

What shape should you memorize for the tangent function's graph over one period?

It has a curve that increases steeply approaching the vertical asymptotes.

What is the relationship between the tangent and cotangent functions?

The cotangent function is the reflection of the tangent function, decreasing as it moves from left to right.

What are the key points for graphing the cosecant function?

Cosecant has vertical asymptotes at integer multiples of π and has a wave-like shape.

Describe how to graph the secant function using the cosine function.

Graph the vertical asymptotes where cosine equals zero; then reflect and stretch the arcs of the cosine graph.

Why are sine and cosine unique among trigonometric functions regarding vertical asymptotes?

Sine and cosine do not have vertical asymptotes, while the other trigonometric functions do due to zeroes in their denominators.

What should students remember about the periods of the cotangent, cosecant, and secant functions?

Cotangent and cosecant both have a period of π, while secant has a period of 2π.