Worksheet: Graphing the Reciprocal Trigonometric Function

In this worksheet, we will practice graphing the tangent function and the arctangent function and describe the features of these graphs.

Q1:

Find the exact value of in radians.

• A
• B
• C
• D
• E

Q2:

Which of these two value tables shows a domain of the tangent function that can be used to construct its inverse function?

Table A

 𝑥 t a n 𝑥 0 𝜋 6 𝜋 4 𝜋 3 9 𝜋 1 9 2 𝜋 3 3 𝜋 4 5 𝜋 6 𝜋 0 1 √ 3 1 √ 3 12.1 − √ 3 − 1 − 1 √ 3 0

Table B

 𝑥 t a n 𝑥 − 9 𝜋 1 9 − 𝜋 3 − 𝜋 4 − 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 9 𝜋 1 9 − 1 2 . 1 − √ 3 − 1 − 1 √ 3 0 1 √ 3 1 √ 3 12.1
• ATable B
• BTable A

Q3:

Which of the following is the graph of ?

• A
• B
• C
• D
• E

Q4:

Which of the following is the graph of ?

• A
• B
• C
• D
• E

Q5:

What is the domain of the function whose graph is shown?

• Aeven integers
• Ball real numbers
• Codd integers
• Dall real numbers except odd integers
• Eall real numbers except even numbers

Q6:

Find the exact value of in radians in the interval .

• A
• B
• C
• D
• E

Q7:

Which of the following is the graph of ?

• A
• B
• C
• D
• E