Functions (trigonometric)

Front

What is the secant function (sec x)?

Back

The secant function is defined as the reciprocal of the cosine function: sec x = 1/cos x.

Front

What happens to sec x when cos x is zero?

Back

When cos x is zero, sec x is undefined because you cannot divide by zero.

Front

What are asymptotes in the context of the secant function?

Back

Asymptotes are lines that the graph approaches but never touches. For sec x, they occur where cos x = 0.

Front

Which trigonometric function has the same asymptotes as sec x?

Back

The secant function has the same asymptotes as the cosecant function.

Front

What is the relationship between sec x and cos x?

Back

Sec x is the reciprocal of cos x, meaning sec x = 1/cos x.

Front

What is the graph of y = sec x characterized by?

Back

The graph of y = sec x has vertical asymptotes and is shaped like a series of U's and inverted U's.

Front

How do you find the vertical asymptotes of sec x?

Back

Vertical asymptotes occur at x = (2n+1)π/2, where n is an integer.

Front

What is the domain of the secant function?

Back

The domain of sec x is all real numbers except for x = (2n+1)π/2, where n is an integer.

Front

What is the range of the secant function?

Back

The range of sec x is (-∞, -1] ∪ [1, ∞).

Front

What is the cosecant function (csc x)?

Back

The cosecant function is defined as the reciprocal of the sine function: csc x = 1/sin x.