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Worksheet: Periodic Functions

Q1:

What is the amplitude of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 ( π‘₯ βˆ’ β„Ž ) ) + π‘˜ s i n ?

  • A π‘Ž + π‘˜
  • B 2 πœ‹ 𝑏
  • C 𝑏
  • D π‘Ž
  • E β„Ž

Q2:

Simplify c o s ( 1 8 0 βˆ’ πœƒ ) ∘ .

  • A s i n πœƒ
  • B c o s πœƒ
  • C βˆ’ πœƒ s i n
  • D βˆ’ πœƒ c o s

Q3:

Simplify s i n ( 1 8 0 βˆ’ πœƒ ) ∘ .

  • A c o s πœƒ
  • B βˆ’ πœƒ s i n
  • C βˆ’ πœƒ c o s
  • D s i n πœƒ

Q4:

What is the amplitude of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 π‘₯ βˆ’ 𝑐 ) + π‘˜ c o s ?

  • A 𝑐
  • B 𝑏
  • C π‘Ž + π‘˜
  • D π‘Ž
  • E 2 πœ‹ 𝑏

Q5:

What is the maximum value of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 ( π‘₯ βˆ’ β„Ž ) ) + π‘˜ s i n ?

  • A π‘Ž
  • B 2 πœ‹ 𝑏
  • C 𝑏
  • D π‘Ž + π‘˜
  • E β„Ž

Q6:

Simplify s i n ( 3 6 0 βˆ’ πœƒ ) ∘ .

  • A c o s πœƒ
  • B s i n πœƒ
  • C βˆ’ πœƒ c o s
  • D βˆ’ πœƒ s i n

Q7:

Let 𝑓 ( π‘₯ ) = 2 π‘₯ s i n . What is the smallest positive value of 𝑃 for which 𝑓 ( π‘₯ + 𝑃 ) = 𝑓 ( π‘₯ ) holds?

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