1. y = sin x
- Amplitude: 1
- Period: 2π
- Key points: (0,0), (π/2,1), (π,0), (3π/2,-1), (2π,0)
- Graph oscillates between y = -1 and y = 1, starting at origin.
2. y = cos x
- Amplitude: 1
- Period: 2π
- Key points: (0,1), (π/2,0), (π,-1), (3π/2,0), (2π,1)
- Graph starts at maximum (0,1), oscillates between y = -1 and y = 1.
3. y = 2 sin x
- Amplitude: 2
- Period: 2π
- Key points: (0,0), (π/2,2), (π,0), (3π/2,-2), (2π,0)
- Vertical stretch by factor of 2; oscillates between y = -2 and y = 2.
4. y = 3 cos x
- Amplitude: 3
- Period: 2π
- Key points: (0,3), (π/2,0), (π,-3), (3π/2,0), (2π,3)
- Vertical stretch by factor of 3; oscillates between y = -3 and y = 3.
5. y = -sin x
- Amplitude: 1
- Period: 2π
- Key points: (0,0), (π/2,-1), (π,0), (3π/2,1), (2π,0)
- Reflection over x-axis; starts at origin, goes down first.
6. y = -2 cos x
- Amplitude: 2
- Period: 2π
- Key points: (0,-2), (π/2,0), (π,2), (3π/2,0), (2π,-2)
- Reflection over x-axis and vertical stretch by 2; starts at minimum (0,-2).
7. y = ½ sin(x - π/2)
- Amplitude: ½
- Period: 2π
- Phase shift: π/2 to the right
- Key points: (π/2,0), (π,½), (3π/2,0), (2π,-½), (5π/2,0)
- Horizontal shift right by π/2, vertical compression by ½.
8. y = cos(2x + π) + 1
- Amplitude: 1
- Period: π (since period = 2π/2)
- Phase shift: π/2 to the left (solve 2x + π = 0 → x = -π/2)
- Vertical shift: up 1 unit
- Key points: (-π/2,0), (0,1), (π/2,0), (π,1), (3π/2,0) — shifted and compressed.
- Oscillates between y = 0 and y = 2.
Parent Tip: Review the logic above to help your child master the concept of trig graphing worksheets.
