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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   x = π/4, π/2, 3π/4, π, 5π/4; y = 1, 4, 1, -2, 1. Pia made this table for one cycle of a moved graph. Which equation matches every row?

   • y = 3 cos(2(x − π/4)) + 1
   • y = 3 sin(2x − π/4) + 1
   • y = 3 sin(2(x + π/4)) + 1
   • y = 3 sin(2(x − π/4)) + 1
2. 2.

   x = π/6, π/3, π/2, 2π/3, 5π/6; y = -7, -4, -1, -4, -7. Ren made this table for one cycle of a moved graph. Which equation matches every row?

   • y = -3 cos(3(x − π/6)) − 4
   • y = -3 cos(3(x + π/6)) − 4
   • y = -3 cos(3x − π/6) − 4
   • y = 3 cos(3(x − π/6)) − 4
3. 3.

   Ari writes y = sin(3x − ☐). Its cycle starts up from the midline at x = 2π/9. What number goes in the box, in terms of π?

   2π/3
4. 4.

   Bo writes y = cos(2x − ☐) + 1. Its cycle has its top row at x = 3π/8. What number goes in the box, in terms of π?

   3π/4
5. 5.

   Esme writes y = 4 sin(4x − ☐). Its cycle starts up from the midline at x = π/12. What number goes in the box, in terms of π?

   π/3
6. 6.

   Jun writes y = -2 cos(5x − ☐) + 3. Its cycle has its bottom row at x = π/10. What number goes in the box, in terms of π?

   π/2
7. 7.

   Kira wants the graph of y = -sin x using sin with a shift. Which equation draws the same graph?

   • y = sin(x + π)
   • y = sin(x + π/2)
   • y = sin(x + 2π)
8. 8.

   Luz wants the graph of y = cos x using sin with a shift. Which equation draws the same graph?

   • y = sin(x + π/2)
   • y = sin(x + π)
   • y = sin(x − π/2)
9. 9.

   Milo wants the graph of y = -cos x using cos with a shift. Which equation draws the same graph?

   • y = cos(x + 2π)
   • y = cos(x + π/2)
   • y = cos(x + π)
10. 10.

    Noah wants the graph of y = sin x using cos with a shift. Which equation draws the same graph?

    • y = cos(x + π/2)
    • y = cos(x − π/2)
    • y = cos(x − π)