Cosecant and Secant Graphs

Front

What is the cosecant function?

Back

The cosecant function, denoted as csc(x), is the reciprocal of the sine function: csc(x) = 1/sin(x).

Front

What is the secant function?

Back

The secant function, denoted as sec(x), is the reciprocal of the cosine function: sec(x) = 1/cos(x).

Front

What is the period of the secant function?

Back

The period of the secant function is 2π.

Front

What is the period of the cosecant function?

Back

The period of the cosecant function is 2π.

Front

What are the vertical asymptotes of the secant function?

Back

The vertical asymptotes of the secant function occur where the cosine function is zero, specifically at x = (2n+1)π/2, where n is an integer.

Front

What are the vertical asymptotes of the cosecant function?

Back

The vertical asymptotes of the cosecant function occur where the sine function is zero, specifically at x = nπ, where n is an integer.

Front

How does the graph of y = sec(x) differ from y = 2sec(x)?

Back

The graph of y = 2sec(x) is a vertical stretch of the graph of y = sec(x) by a factor of 2.

Front

How does the graph of y = csc(x) differ from y = -csc(x)?

Back

The graph of y = -csc(x) is a reflection of the graph of y = csc(x) across the x-axis.

Front

What is the range of the secant function?

Back

The range of the secant function is (-∞, -1] ∪ [1, ∞).

Front

What is the range of the cosecant function?

Back

The range of the cosecant function is (-∞, -1] ∪ [1, ∞).