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 downward first.
6. y = -2 cos x
- Amplitude: 2
- Period: 2π
- Key points: (0,-2), (π/2,0), (π,2), (3π/2,0), (2π,-2)
- Vertical stretch by 2 and reflection over x-axis; 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: +1 (whole graph shifted up by 1 unit)
- Key points: (-π/2,2), (0,0), (π/2,2), (π,0), (3π/2,2)
- Oscillates between y=2 and y=0, with period π, shifted left by π/2 and up by 1.
Parent Tip: Review the logic above to help your child master the concept of graphing trig functions worksheets.
