Worksheet: Graphs of Trigonometric Functions

In this worksheet, we will practice graphing trigonometric functions, such as sine and cosine, and deducing their properties.

Q1:

What is the maximum value of 𝑓 ( 𝑥 ) = 𝑥 s i n ?

Q2:

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

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

Q3:

Assign each plot shown in the graph below to the function it represents.

  • A the red plot: cosine, the blue plot: tangent
  • B the red plot: tangent, the blue plot: sine
  • C the red plot: sine, the blue plot: cosine
  • D the red plot: cosine, the blue plot: sine
  • Ethe red plot: tangent, the blue plot: cosine

Q4:

What is the minimum value of 𝑓 ( 𝑥 ) = 𝑥 c o s ?

Q5:

Complete the following table:

𝜃 0 𝜋 6 3 𝜋 6 5 𝜋 6 𝜋 7 𝜋 6 9 𝜋 6 1 1 𝜋 6 2 𝜋
s i n 𝜃 0 0.5 0.5 0 0 . 5 1 0 . 5 0

Q6:

Which of the following is the graph of 𝑦 = 2 𝑥 s i n ?

  • A
  • B
  • C
  • D
  • E

Q7:

What is the maximum value of 𝑓 ( 𝑥 ) = 5 4 𝜋 𝑥 7 5 + 1 2 c o s ?

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

Q8:

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

Q9:

Which of the following is the graph of 𝑦 = ( 𝑥 ) + 1 s i n ?

  • A
  • B
  • C
  • D
  • E

Q10:

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

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

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