The graph of y = sin x is a wave that starts at the origin, rises to 1 at π/2 and repeats every 2π.
| Domain | All real numbers (ℝ) |
| Range | [−1, 1] |
| Symmetry | Odd: symmetric about the origin |
| Increasing / decreasing | Repeats every 2π (period 2π) |
| Key feature | Zeros at x = nπ; maximum 1 at x = π/2 + 2nπ |
In y = a sin(x − h) + k, the wave moves h right and its centre line moves to y = k; a sets the height (amplitude |a|).
a stretches the graph vertically and flips it when negative. h shifts it right (left when negative). k shifts it up (down when negative).
Can you spot a transformed sin x?Play Vakra: name the curve in five plots