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 𝑓(𝑥)=1(𝑥)sin?

  • A
  • B
  • C
  • D

Q2:

Consider the graph of 𝑦=𝑥sin, as shown in the figure. We are going to use the graph to help us identify some key features of the graph of 𝑦=𝑥cosec.

Use the fact that cosecsin𝑥=1𝑥 to determine whether each of the points 𝐴, 𝐵, 𝐶, and 𝐷 will represent the position of an asymptote, a local maximum, or a local minimum on the graph of 𝑦=𝑥cosec.

  • AAsymptote: 𝐴 and 𝐶, local maximum: 𝐵, local minimum: 𝐷
  • BAsymptote: 𝐴 and 𝐷, local maximum: 𝐵, local minimum: 𝐶
  • CAsymptote: 𝐴 and 𝐶, local maximum: 𝐷, local minimum: 𝐵
  • DAsymptote: 𝐵 and 𝐷, local maximum: 𝐴, local minimum: 𝐶
  • EAsymptote: 𝐴 and 𝐵, local maximum: 𝐶, local minimum: 𝐷

Identify which of the following is the graph of 𝑦=𝑥cosec.

  • A
  • B
  • C
  • D
  • E