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 range of the cosecant function, y = csc(x)?

Back

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

Front

What is the range of the secant function, y = sec(x)?

Back

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

Front

How does the amplitude of a trigonometric function affect its graph?

Back

The amplitude of a trigonometric function determines the height of its peaks and the depth of its troughs. For example, an amplitude of 4 means the graph reaches 4 units above and below the midline.

Front

What is the maximum value of a trigonometric function with an amplitude of 4 and a minimum value of 5?

Back

The maximum value is 5 (minimum) + 4 (amplitude) = 9.

Front

What is the period of the cosecant and secant functions?

Back

The period of both cosecant and secant functions is 2π.

Front

How do you find the vertical asymptotes of the secant function?

Back

Vertical asymptotes of sec(x) occur where cos(x) = 0, which is at x = (2n+1)π/2, where n is an integer.

Front

What is the relationship between the sine and cosecant functions?

Back

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

Front

What is the relationship between the cosine and secant functions?

Back

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