Graph sine and cosine, and read amplitude, period, midline and phase shift

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Jun compares y = cos(2x + π/3) − 2 with y = cos(2x) − 2. Which way and how far are the rows moved?

   • right π/6
   • left π/3
   • left π/6
   • right π/3
2. 2.

   Kira compares y = -3 sin(4x + π/2) with y = -3 sin(4x). Which way and how far are the rows moved?

   • right π/2
   • left π/8
   • left π/2
   • right π/8
3. 3.

   x = π/6, 5π/12, 2π/3, 11π/12, 7π/6; y = 5, 2, -1, 2, 5. Milo made this table for one cycle of a shifted sine graph. What is the period, in terms of π?

   π
4. 4.

   x = π/4, 3π/4, 5π/4, 7π/4, 9π/4; y = 3, -1, -5, -1, 3. Noah made this table for one cycle of a shifted sine graph. What is the period, in terms of π?

   2π
5. 5.

   x = π/2, 2π/3, 5π/6, π, 7π/6; y = 6, 4, 2, 4, 6. Pia made this table for one cycle of a shifted sine graph. What is the period, in terms of π?

   2π/3
6. 6.

   x = π/3, 7π/12, 5π/6, 13π/12, 4π/3; y = -4, 0, 4, 0, -4. Ren made this table for one cycle of a shifted sine graph. What is the period, in terms of π?

   π
7. 7.

   Zee graphs y = -3 sin(2x − π/2) + 4. What is the greatest value of y?

   7
8. 8.

   Ari graphs y = 5 cos(3x + π) − 4. What is the least value of y?

   -9
9. 9.

   Bo graphs y = -6 cos(x/2 + π/4) − 1. What is the greatest value of y?

   5
10. 10.

    Esme graphs y = 4 sin(3x − 3π/4) + 9. What is the least value of y?

    5