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. 1.

   “Graph plotted from its table:” Jun writes y = ☐ sin(2x) + 1 for this graph. What number goes in the box?

   4
2. 2.

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

   6
3. 3.

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

   -3
4. 4.

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

   4
5. 5.

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

   3
6. 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)
7. 7.

   Ari moves the row (270, -1) of y = sin x, with x in degrees. Where does it land on y = sin(x + 60°) + 5?

   (210, 4)
8. 8.

   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. 9.

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

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

    Luz makes y = -sin(x − π/6) − 1 from the table of y = sin x. Which moves does it make?

    • flip upside down, then left π/6, then up 1
    • flip upside down, then right π/6, then down 1
    • flip upside down, then left π/6, then down 1
    • right π/6, then down 1