- For y = sin(x - π/4) + 4: The graph is the standard sine wave shifted right by π/4 and up by 4 units. The midline is y=4, amplitude is 1, period is 2π. Key points: (π/4, 4), (3π/4, 5), (5π/4, 4), (7π/4, 3), (9π/4, 4).
- For y = sin(x + π/2) - 3: The graph is the standard sine wave shifted left by π/2 and down by 3 units. The midline is y=-3, amplitude is 1, period is 2π. Key points: (-π/2, -3), (0, -2), (π/2, -3), (π, -4), (3π/2, -3).
- For y = sin(x - π) + 1: The graph is the standard sine wave shifted right by π and up by 1 unit. The midline is y=1, amplitude is 1, period is 2π. Key points: (π, 1), (3π/2, 2), (2π, 1), (5π/2, 0), (3π, 1).
- For y = sin(x - π) + 4: The graph is the standard sine wave shifted right by π and up by 4 units. The midline is y=4, amplitude is 1, period is 2π. Key points: (π, 4), (3π/2, 5), (2π, 4), (5π/2, 3), (3π, 4).
- For y = 2·sin(2x): The graph has an amplitude of 2 and a period of π. The midline is y=0. Key points: (0, 0), (π/4, 2), (π/2, 0), (3π/4, -2), (π, 0).
- For y = 4·sin(2x): The graph has an amplitude of 4 and a period of π. The midline is y=0. Key points: (0, 0), (π/4, 4), (π/2, 0), (3π/4, -4), (π, 0).
Parent Tip: Review the logic above to help your child master the concept of graphs of trigonometric functions worksheet.
