Worksheet: Horizontal and Vertical Shifts of Sine and Cosine

In this worksheet, we will practice translating sine and cosine graphs through horizontal and vertical shifts.

Q1:

The figure shows the graph of a function. Which of the following equations represents the graph?

  • A 𝑦 = 2 𝑥 s i n
  • B 𝑦 = 2 𝑥 s i n
  • C 𝑦 = 𝑥 + 2 s i n
  • D 𝑦 = ( 𝑥 + 2 ) s i n
  • E 𝑦 = ( 𝑥 2 ) s i n

Q2:

Which of the following equations is represented by the given graph?

  • A 𝑦 = ( 𝑥 + 2 ) s i n
  • B 𝑦 = 2 𝑥 s i n
  • C 𝑦 = 𝑥 + 2 s i n
  • D 𝑦 = 2 𝑥 s i n s
  • E 𝑦 = ( 𝑥 2 ) s i n

Q3:

Which of the following is the graph of 𝑦 = ( 𝑥 9 0 ) s i n ?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following is the graph of 𝑦 = ( 𝑥 9 0 ) c o s ?

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is the graph of 𝑦 = 𝑥 4 1 s i n ?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following is the graph of 𝑦 = ( 3 𝑥 + 9 0 ) s i n ?

  • A
  • B
  • C
  • D