Math
Sine and cosine graphs.
Definition
The graphs of y = sin(x) and y = cos(x) are smooth, wave-shaped curves that repeat every 2π. The sine graph starts at the origin and the cosine graph starts at its maximum. Both have an amplitude of 1 and can be transformed by changing amplitude, period, phase shift, and vertical shift.
Examples
Real-world.
- 1 y = sin(x) crosses zero at 0, π, and 2π, and reaches its peak of 1 at π/2
- 2 y = 2cos(3x) has amplitude 2 and period 2π/3
- 3 Sound waves can be modeled using sine and cosine graphs
Key Fact
Period of y = sin(Bx) or y = cos(Bx) is 2π/|B|