Lesson 17 Graphing Cosecant and Secant

Front

What is the cosecant function?

Back

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

Front

What is the secant function?

Back

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

Front

How does a vertical stretch affect the graph of a function?

Back

A vertical stretch by a factor of \( k \) multiplies the y-values of the function by \( k \), making the graph taller.

Front

What is a horizontal stretch in graph transformations?

Back

A horizontal stretch by a factor of \( k \) compresses the x-values of the function by a factor of \( k \), making the graph wider.

Front

What does reflecting a graph across the x-axis do?

Back

Reflecting a graph across the x-axis changes the sign of the y-values, effectively flipping the graph upside down.

Front

How do you identify the period of the cosecant function \( \csc(kx) \)?

Back

The period of \( \csc(kx) \) is given by \( \frac{2\pi}{|k|} \). For \( \csc(2x) \), the period is \( \pi \).

Front

What is the relationship between the cosecant and sine functions?

Back

The cosecant function is undefined wherever the sine function is zero, as it involves division by zero.

Front

How do you graph \( y = 3\csc(2x) \)?

Back

Start with the graph of \( \csc(2x) \), apply a vertical stretch by 3, and note that the period is \( \pi \).

Front

What transformations are applied to the graph of \( y = \csc(x) \) to obtain \( y = 3\csc(2x) \)?

Back

The transformations include a vertical stretch by 3 and a horizontal compression by a factor of 2.

Front

What is the period of the secant function \( \sec(kx) \)?

Back

The period of \( \sec(kx) \) is \( \frac{2\pi}{|k|} \). For \( \sec(2x) \), the period is \( \pi \).