Write sine and cosine equations from graphs, and shifts and flips

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Use this

   Graph plotted from its table:

2. 1.

   Jun writes y = ☐ sin(2x) + 1 for this graph. What number goes in the box?

   4
3. 2.

   Kira writes y = 3 cos(x/2) + ☐ for this graph. What number goes in the box?

   4
4. 3.

   Milo writes y = 5 sin(4x) + ☐ for this graph. What number goes in the box?

   -3
5. 4.

   Noah writes y = 3 sin(☐x) − 1 for a graph with period 90°, x in degrees. What number goes in the box?

   4
6. 5.

   Pia writes y = cos(☐x) + 2 for a graph with period 120°, x in degrees. What number goes in the box?

   3
7. 6.

   Zee moves the row (0, 1) of y = cos x, with x in degrees. Where does it land on y = cos(x + 45°) − 3?

   (-45, -2)
8. 7.

   Bo moves the row (180, -1) of y = cos x, with x in degrees. Where does it land on y = cos(x − 90°) − 1?

   (270, -2)
9. 8.

   Esme makes y = sin(x − π/4) + 3 from the table of y = sin x. Which moves does it make?

   • right 3, then up π/4
   • left π/4, then up 3
   • right π/4, then down 3
   • right π/4, then up 3
10. 9.

    Jun makes y = -cos x + 2 from the table of y = cos x. Which moves does it make?

    • left 2
    • flip upside down, then down 2
    • flip upside down, then up 2
    • up 2
11. 10.

    Kira makes y = cos(x + π/3) − 4 from the table of y = cos x. Which moves does it make?

    • right π/3, then down 4
    • left 4, then down π/3
    • left π/3, then up 4
    • left π/3, then down 4