Write sine and cosine equations from graphs, and shifts and flips
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
Milo wants a graph with amplitude 3, period π, midline y = -1, starting at the top at x = 0. Which equation is it?
- y = 3 cos(πx) − 1
- y = 3 sin(2x) − 1
- y = -cos(2x) + 3
- y = 3 cos(2x) − 1
Noah wants a graph with amplitude 2, period 4π, midline y = 5, starting on the midline going up at x = 0. Which equation is it?
- y = 2 sin(x/2) + 5
- y = 5 sin(x/2) + 2
- y = 2 cos(x/2) + 5
- y = 2 sin(4πx) + 5
Pia wants a graph with amplitude 4, period 2π/3, midline y = 1, starting at the bottom at x = 0. Which equation is it?
- y = -4 sin(3x) + 1
- y = -4 cos(3x) + 1
- y = -cos(3x) + 4
- y = -4 cos(2πx/3) + 1
x = 0, π/4, π/2, 3π/4, π; y = -5, -2, 1, -2, -5. Zee made this table for one cycle of a graph. Which equation matches every row?
- y = -6 cos(2x) − 2
- y = 3 cos(2x) − 2
- y = -3 cos(πx) − 2
- y = -3 cos(2x) − 2
x = 0, π/6, π/3, π/2, 2π/3; y = 2, -1, 2, 5, 2. Bo made this table for one cycle of a graph. Which equation matches every row?
- y = -3 sin(2πx/3) + 2
- y = -3 sin(3x) + 2
- y = -6 sin(3x) + 2
- y = 3 sin(3x) + 2
x = 0, π/8, π/4, 3π/8, π/2; y = 6, 3, 0, 3, 6. Esme made this table for one cycle of a graph. Which equation matches every row?
- y = 3 cos(4x) + 3
- y = 3 cos(πx/2) + 3
- y = 6 cos(4x) + 3
- y = 3 sin(4x) + 3
Jun graphs y = 2 sin(3x − 2π/3) + 1. To what x does the row that was at x = 0 move?
Kira graphs y = cos(2x − 5π/6) − 3. To what x does the row that was at x = 0 move?
Luz graphs y = -4 sin(3x + 2π/3) + 1. To what x does the row that was at x = 0 move?
Milo graphs y = 5 cos(2x + 3π/4). To what x does the row that was at x = 0 move?