Sin and Cos Graphs

The period is the distance along the x-axis for one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

The amplitude is the maximum distance from the midline of the graph to the peak (or trough). It is the coefficient in front of the sine or cosine function.

A represents the amplitude, and B affects the period of the function. The period is calculated as 2π/B.

The period is calculated as 2π/k, where k is the coefficient of x.

A negative sign reflects the graph across the x-axis.

Sine functions start at the midline (0) and go up, while cosine functions start at the maximum value (A) and go down.

y = 2 sin(x) represents a sine function with an amplitude of 2.

y = cos(2x) has a period of π, since the period is 2π/2 = π.

The value of k affects the frequency and period of the graph. Higher values of k result in more cycles in the same interval.

The midline is the horizontal line that runs through the middle of the wave, typically at y = 0 unless shifted vertically.