Sine and Cosine Graphs

The sine function, denoted as sin(x), is a periodic function that describes the y-coordinate of a point on the unit circle corresponding to an angle x. It has a range of [-1, 1] and a period of 2π.

The cosine function, denoted as cos(x), is a periodic function that describes the x-coordinate of a point on the unit circle corresponding to an angle x. It has a range of [-1, 1] and a period of 2π.

The amplitude is the maximum distance from the midline of the graph to its peak or trough. For f(x) = A sin(Bx) or f(x) = A cos(Bx), the amplitude is |A|.

The period is the length of one complete cycle of the graph. For f(x) = A sin(Bx) or f(x) = A cos(Bx), the period is given by 2π/|B|.

A vertical shift moves the graph up or down. For f(x) = A sin(Bx) + D or f(x) = A cos(Bx) + D, D represents the vertical shift.

A sine graph starts at the midline (0) and goes up, while a cosine graph starts at its maximum value (A).

A negative sign in front of the cosine function reflects the graph across the x-axis. For example, y = -cos(x) is a reflection of y = cos(x).

The phase shift is the horizontal shift left or right for the graph. For f(x) = A sin(B(x - C)) or f(x) = A cos(B(x - C)), the phase shift is C.

The equation is f(x) = A sin(Bx) + D, where D is the vertical shift.

The equation is f(x) = A cos(Bx) + D, where D is the vertical shift.