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?

s i n 𝜃 = 1 . 2 .

  • AImpossible
  • BPossible

Q2:

Is the following statement possible or impossible?

c o s 𝜃 = − 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?

c o t 𝜃 = − 2 .

  • AImpossible
  • BPossible

Q5:

Is the following statement possible or impossible?

c s c 𝜃 = − 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 − 5 4
  • B − 3
  • C 5 4
  • D3

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