Worksheet: Amplitude and Period of Trigonometric Functions

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In this worksheet, we will practice finding the amplitude and the period of sine, cosine, and tangent functions.

Q1:

Determine the amplitude and the period of the shown function.

  • Aamplitude = 6 , period = 1
  • Bamplitude = − 3 , period = 2
  • Camplitude = 6 , period = 3
  • Damplitude = 3 , period = 2
  • Eamplitude = 3 , period = 1

Q2:

What is the period of 𝑓 ( 𝑥 ) = 2 𝑥 + 𝜋 3 s i n ?

  • A 3 𝜋
  • B 𝜋 3
  • C 2 𝜋
  • D 6 𝜋
  • E 5 𝜋

Q3:

What is the period of 𝑓 ( 𝑥 ) = 2 𝑥 c o s ?

  • A 𝜋 2
  • B 2 𝜋
  • C 𝜋 4
  • D 𝜋
  • E 𝜋 3

Q4:

What is the period of 𝑓 ( 𝑥 ) = 2 3 3 𝑥 4 c o s ?

  • A 8 𝜋
  • B 2 𝜋
  • C 2 𝜋 3
  • D 8 𝜋 3
  • E 3 𝜋 4

Q5:

Find the period of the function 𝑓 ( 𝜃 ) = 1 1 4 𝜃 s i n .

  • A 2 𝜋 1 1
  • B 2 𝜋
  • C 1 1 𝜋 2
  • D 𝜋 2

Q6:

What is the period of the function 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 𝑥 − 𝑐 ) + 𝑘 c o s ?

  • A 𝑏 2 𝜋
  • B 𝑎
  • C 𝑏
  • D 2 𝜋 𝑏
  • E 𝑐

Q7:

What is the period of 𝑓 ( 𝑥 ) = 3 2 𝑥 − 𝜋 5 t a n ?

  • A 3 𝜋
  • B 𝜋 5
  • C 2 𝜋 5
  • D 5 𝜋 2
  • E 6 𝜋

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