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Worksheet: Amplitude and Period of Trigonometric Functions

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 = βˆ’ 3 , period = 2
  • Camplitude = 6 , period = 3
  • Damplitude = 3 , period = 2
  • Eamplitude = 3 , period = 1

Q2:

What is the amplitude of 𝑓 ( π‘₯ ) = 5 4 ο€» πœ‹ π‘₯ 7 βˆ’ 5  + 1 2 c o s ?

  • A5
  • B14
  • C12
  • D 5 4
  • E πœ‹ 7

Q3:

Find the period of the function 𝑓 ( πœƒ ) = 1 1 4 πœƒ s i n .

  • A 2 πœ‹ 1 1
  • B 2 πœ‹
  • C 1 1 πœ‹ 2
  • D πœ‹ 2

Q4:

The range of the function is . Find the value of where .

  • A
  • B3
  • C
  • D

Q5:

s i n π‘₯ has period 2 πœ‹ and t a n π‘₯ has period πœ‹ . What is the period of their sum s i n t a n π‘₯ + π‘₯ ?

  • A 3 2 πœ‹
  • B πœ‹
  • C πœ‹ and 2 πœ‹
  • D 2 πœ‹
  • E 3 πœ‹

Q6:

What is the amplitude of the function 𝑦 = βˆ’ 5 ( 4 π‘₯ + 3 ) s i n ?

Q7:

What is the amplitude of 𝑓 ( π‘₯ ) = π‘₯ s i n ?

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