# Worksheet: The Graphs of Reciprocal Trigonometric Functions

In this worksheet, we will practice graphing cosecant, secant, and cotangent functions by understanding that they are related to the graphs of the sine, cosine, and tangent functions.

Q1:

Which of the following is the graph of the function ?

• A • B • C • D Q2:

Consider the graph of , as shown in the figure. We are going to use the graph to help us identify some key features of the graph of . Use the fact that to determine whether each of the points , , , and will represent the position of an asymptote, a local maximum, or a local minimum on the graph of .

• AAsymptote: and , local maximum: , local minimum:
• BAsymptote: and , local maximum: , local minimum:
• CAsymptote: and , local maximum: , local minimum:
• DAsymptote: and , local maximum: , local minimum:
• EAsymptote: and , local maximum: , local minimum:

Identify which of the following is the graph of .

• A • B • C • D • E Q3:

Identify the graph of .

• A • B • C • D • E Q4:

Identify the graph of .

• A • B • C • D • E Q5:

The three graphs shown represent the functions , , and . The function is represented by the graph C. Which of the following is the equation of ?

• A
• B
• C
• D
• E

The function is represented by the graph A. Which of the following is the equation of ?

• A
• B
• C
• D
• E

The function is represented by the graph B. Which of the following is the equation of ?

• A
• B
• C
• D
• E

Q6:

Consider the graph of as shown in the figure. We are going to use the graph to help us identify some key features of the graph of . Use the fact that to determine which points from , , , and can be used to identify the position of an asymptote, a local maximum, or a local minimum on the graph of .

• AAsymptote: , local maximum: and , local minimum:
• BAsymptote: , local maximum: and , local minimum:
• CAsymptote: , local maximum: and , local minimum:
• DAsymptote: and , local maximum: and
• EAsymptote: , local maximum: , local minimum: and

Identify which of the following is the graph of .

• A • B • C • D • E Q7:

Consider the graph of as shown in the figure. We are going to use the graph to help us identify some key features of the graph of . Use the fact that to determine which of the points , , , and can be used to identify the position of an asymptote, a zero, a positive, or a negative on the graph of .

• AAsymptote: , zero: , positive: , negative:
• BAsymptote: , zero: , positive: , negative:
• CAsymptote: , zero: , positive: , negative:
• DAsymptote: , zero: , positive: , negative:
• EAsymptote: , zero: , positive: , negative:

Identify which of the following is the graph of .

• A • B • C • D • E 