Write sine and cosine equations from graphs, and shifts and flips
Grade 11 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
x = π/6, 5π/12, 2π/3, 11π/12, 7π/6; y = 5, 2, -1, 2, 5. Noah made this table for one cycle of a moved graph. Which equation matches every row?
- y = 3 cos(2(x + π/6)) + 2
- y = 3 cos(2(x − π/6)) + 2
- y = 3 cos(2x − π/6) + 2
- y = 3 sin(2(x − π/6)) + 2
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(2(x + π/4)) + 1
- y = 3 sin(2x − π/4) + 1
- y = 3 sin(2(x − π/4)) + 1
x = π/8, 3π/8, 5π/8, 7π/8, 9π/8; y = -2, 1, 4, 1, -2. Zee made this table for one cycle of a moved graph. Which equation matches every row?
- y = -3 cos(2(x − π/8)) + 1
- y = -3 cos(2x − π/8) + 1
- y = -3 cos(2(x + π/8)) + 1
- y = 3 cos(2(x − π/8)) + 1
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?
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?
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?
Kira wants the graph of y = -sin x using sin with a shift. Which equation draws the same graph?
- y = sin(x + 2π)
- y = sin(x + π)
- y = sin(x + π/2)
Luz wants the graph of y = cos x using sin with a shift. Which equation draws the same graph?
- y = sin(x + π)
- y = sin(x − π/2)
- y = sin(x + π/2)
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)
- y = cos(x + π/2)
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)
- y = cos(x + π/2)