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 t a n t a n 1 5 𝜋 6 in radians.

  • A 5 𝜋 6
  • B 7 𝜋 6
  • C 𝜋 6
  • D 𝜋 6
  • E 𝜋

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

Table B

𝑥 9 𝜋 1 9 𝜋 3 𝜋 4 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 9 𝜋 1 9
t a n 𝑥 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 𝑦 = 𝑥 t a n ?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following is the graph of 𝑦 = ( 𝑥 + 9 0 ) t a n ?

  • A
  • B
  • C
  • D
  • E

Q5:

What is the domain of the function t a n 𝜋 𝑥 2 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 t a n 1 ( 1 ) in radians in the interval 𝜋 < 𝜃 2 𝜋 3 .

  • A 3 𝜋 2
  • B 2 𝜋 3
  • C 1
  • D 𝜋 4
  • E 𝜋 2

Q7:

Which of the following is the graph of 𝑦 = ( 𝑥 ) t a n ?

  • A
  • B
  • C
  • D
  • E