Lesson Worksheet: Domain and Range of Trigonometric Functions Mathematics

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

Q1:

Find the domain of the function 𝑓(𝜃)=5(𝜃)+4sin.

  • A(−∞,∞)
  • B[−1,9]
  • C(−5,5)
  • D(−1,9)
  • E[−5,5]

Q2:

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

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

Q3:

Consider the function 𝑓(𝑥)=4(7𝑥+𝜋)+5cos.

What is the domain of 𝑓(𝑥)?

  • A(−∞,∞)
  • B(−7,7)
  • C(−4,4)
  • D(−8,8)
  • E(−5,5)

What is the range of 𝑓(𝑥)?

  • A[−4,6]
  • B[1,9]
  • C[−1,1]
  • D[−1,2]
  • E[−4,4]

Q4:

Find the range of the function 𝑓(𝜃)=3(𝜃)+4sin.

  • A[−3,3]
  • B(1,7)
  • C[1,7]
  • D[−1,1]
  • E(−3,3)

Q5:

Consider the following graph of 𝑓(𝜃).

What is the domain of 𝑓(𝜃)?

  • A(−∞,∞)
  • B[0,2𝜋]
  • C[−4,6]
  • D−𝜋2,𝜋2
  • E(−4,6)

What is the range of 𝑓(𝜃)?

  • A−𝜋2,𝜋2
  • B(−4,6)
  • C[−4,6]
  • D[0,2𝜋]
  • E(−∞,∞)

Q6:

The following graph shows the function 𝑓(𝜃). Assume the function has a period of 2𝜋.

What is the domain of 𝑓(𝜃)?

  • A(−∞,∞)
  • B(0,∞)
  • C(−∞,0)
  • D(0,1)
  • E(−1,1)

What is the range of 𝑓(𝜃)?

  • A[0,3]
  • B[3,7]
  • C[−7,3]
  • D(−∞,∞)
  • E[−1,1]

Q7:

Is the following statement possible or impossible?

sin𝜃=1.2.

  • AImpossible
  • BPossible

Q8:

The range of the function 𝑓(𝜃)=𝑎(2𝜃)sin is [−5,5]. Find the value of 𝑎, where 𝑎>0.

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

Q10:

Find the values of 𝜃 in radians such that the function 𝑓(𝜃)=(3𝜃)tan is undefined.

  • A𝜋6+𝑛𝜋3
  • B𝜋6+𝑛𝜋6
  • C𝜋2+2𝑛𝜋
  • D𝜋2+𝑛𝜋
  • E𝜋4+𝑛𝜋4

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