The graph of y = cos x is the sin wave shifted π/2 to the left: it starts at its top, 1, when x = 0.
| Domain | All real numbers (ℝ) |
| Range | [−1, 1] |
| Symmetry | Even: symmetric about the y-axis |
| Increasing / decreasing | Repeats every 2π (period 2π) |
| Key feature | Maximum 1 at x = 2nπ; zeros at x = π/2 + nπ |
In y = a cos(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 cos x?Play Vakra: name the curve in five plots