Sine and Cosine Graphs

The equation can be expressed as y = A cos(Bx) + D, where D is the vertical shift. For example, y = -3 cos x - 4 has a vertical shift of -4.

The period of a sine or cosine function is given by the formula T = 2π/|B|, where B is the coefficient of x in the function y = A sin(Bx) or y = A cos(Bx).

If the graph starts at its maximum or minimum value, it is a cosine function. If it starts at zero and goes up or down, it is a sine function.

The equation can be expressed as y = 2 sin(x), where the amplitude is the coefficient of the sine function.

The coefficient of x (B) affects the period. The period is calculated as T = 2π/|B|. A larger B results in a shorter period.

The amplitude is the absolute value of the coefficient in front of the cosine function, which is 4.

The vertical shift is 3, which moves the graph up by 3 units.

The equation can be expressed as y = A cos(B(x - C)), where C is the phase shift. For example, y = 2 cos(3(x - π/2)) has a phase shift of π/2 to the right.

The maximum value is A + D and the minimum value is -A + D, where A is the amplitude and D is the vertical shift.

The period is T = 2π/|5| = 2π/5.