Worksheet: Domain and Range of Trigonometric Functions

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In this worksheet, we will practice determining the domain and range of a trigonometric function.

Q1:

Is the following statement possible or impossible?

sin𝜃=1.2.

  • AImpossible
  • BPossible

Q2:

Is the following statement possible or impossible?

cos𝜃=−3.1.

  • AImpossible
  • BPossible

Q3:

Is it possible for tan𝜃 to be equal to −125?

  • ANo, it is impossible.
  • BYes, it is possible.

Q4:

Is the following statement possible or impossible?

cot𝜃=−2.

  • AImpossible
  • BPossible

Q5:

Is the following statement possible or impossible?

csc𝜃=−2.4.

  • APossible
  • BImpossible

Q6:

Is the statement sec𝜃=0.9 possible or impossible?

  • AImpossible
  • BPossible

Q7:

Find the range and period of the function 𝑓(𝜃)=1454𝜃sin by drawing the function between 0 and 2𝜋.

  • Arange=0,145, period=𝜋2
  • Brange=[−1,1], period=𝜋2
  • Crange=−145,145, period=2𝜋
  • Drange=−145,145, period=𝜋2

Q8:

Find the range of the function 𝑓(𝜃)=87𝜃sin.

  • A[−7,7]
  • B[0,1]
  • C[0,8]
  • D[−8,8]
  • E[−1,1]

Q9:

The range of the function 𝑓(𝜃)=𝑎3𝜃cos is −54,54. Find the value of 𝑎 where 𝑎>0.

  • A−54
  • B−3
  • C54
  • D3

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