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Worksheet: Graphs of Trigonometric Functions

Q1:

Find the minimum and maximum values of the function 𝑓 ( πœƒ ) = 1 3 6 9 πœƒ s i n by drawing the function.

  • A minimum value = βˆ’ 1 , maximum value = 1
  • Bminimum value = βˆ’ 9 , maximum value = 9
  • C minimum value = 0 , maximum value = 1 3 6
  • D minimum value = βˆ’ 1 3 6 , maximum value = 1 3 6

Q2:

Which of the following is the graph of 𝑦 = 2 π‘₯ s i n ?

  • A
  • B
  • C
  • D
  • E

Q3:

Identify the graph of 𝑦 = π‘₯ c o s e c .

  • A
  • B
  • C
  • D
  • E

Q4:

Complete the following table:

πœƒ 0 πœ‹ 6 3 πœ‹ 6 5 πœ‹ 6 πœ‹ 7 πœ‹ 6 9 πœ‹ 6 1 1 πœ‹ 6 2 πœ‹
s i n πœƒ 0 0.5 β‹― 0.5 0 βˆ’ 0 . 5 βˆ’ 1 βˆ’ 0 . 5 0

Q5:

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

  • A 4 3 4
  • B14
  • C5
  • D 5 3 4
  • E12

Q6:

What is the minimum value of the function 𝑓 ( π‘₯ ) = 5 ( 4 π‘₯ + 6 ) + 8 c o s ?

Q7:

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

Q8:

Which of the following is the graph of 𝑦 = ( π‘₯ ) + 1 s i n ?

  • A
  • B
  • C
  • D
  • E

Q9:

Find the minimum value of the function 𝑓 ( πœƒ ) = 2 0 9 3 πœƒ s i n .

  • A βˆ’ 3
  • B 2 0 9
  • C 1
  • D βˆ’ 2 0 9
  • E 3

Q10:

What is the frequency of the function 𝑓 ( 𝑑 ) = 3 4 ο€Ό 3 πœ‹ 𝑑 5  + 4 πœ‹ s i n ?

  • A 3 4
  • B 1 0 3
  • C 3 πœ‹ 5
  • D 3 1 0
  • E 4 πœ‹