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Worksheet: The Graphs of Reciprocal Trigonometric Functions

Q1:

Consider the graph of 𝑦 = 𝑥 s i n , as shown in the figure. We are going to use the graph to help us identify some key features of the graph of 𝑦 = 𝑥 c o s e c .

Use the fact that c o s e c s i n 𝑥 = 1 𝑥 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 = 𝑥 c o s e c .

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

Identify which of the following is the graph of 𝑦 = 𝑥 c o s e c .

  • A
  • B
  • C
  • D
  • E

Q2:

Identify the graph of 𝑦 = 𝑥 s e c .

  • A
  • B
  • C
  • D
  • E

Q3:

Identify the graph of 𝑦 = 𝑥 c o t .

  • A
  • B
  • C