6.5 Graphs of Tan, Cot, Csc, and Sec

Front

What is the graph of y = tan(x)?

Back

The graph of y = tan(x) has vertical asymptotes at x = (2n+1)π/2, where n is an integer, and it has a period of π.

Front

What is the range of y = csc(x)?

Back

The range of y = csc(x) is (-∞, -1] ∪ [1, ∞).

Front

What does the function y = cot(x) represent?

Back

The function y = cot(x) is the reciprocal of the tangent function, defined as cot(x) = 1/tan(x). It has vertical asymptotes at x = nπ, where n is an integer.

Front

What is the effect of a negative A value in y = A sin(Bx)?

Back

A negative A value causes a reflection across the x-axis.

Front

What is the period of y = sec(x)?

Back

The period of y = sec(x) is 2π.

Front

What are the asymptotes of y = sec(x)?

Back

The asymptotes of y = sec(x) occur at x = (2n+1)π/2, where n is an integer.

Front

How does the graph of y = tan(x + π/4) differ from y = tan(x)?

Back

The graph of y = tan(x + π/4) is a horizontal shift of the graph of y = tan(x) to the left by π/4.

Front

What is the relationship between the graphs of y = csc(x) and y = sin(x)?

Back

The graph of y = csc(x) is the reciprocal of the graph of y = sin(x), with vertical asymptotes where sin(x) = 0.

Front

What is the domain of y = cot(x)?

Back

The domain of y = cot(x) is all real numbers except x = nπ, where n is an integer.

Front

What is the effect of changing the value of B in y = A sin(Bx)?

Back

Changing the value of B affects the period of the function; the period is given by 2π/|B|.