TE Sin and Cos Graphs

The sine function, denoted as sin(x), is a periodic function that describes the y-coordinate of a point on the unit circle as it rotates around the origin. It oscillates between -1 and 1.

The cosine function, denoted as cos(x), is a periodic function that describes the x-coordinate of a point on the unit circle as it rotates around the origin. It oscillates between -1 and 1.

The amplitude is the maximum distance from the midline (equilibrium position) to the peak (maximum) or trough (minimum) of the graph. It is half the distance between the maximum and minimum values.

The period is the length of one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

In this equation, A represents the amplitude, B affects the period of the function, and x is the variable. The period can be calculated as 2π/B.

Similar to the sine function, in this equation, A represents the amplitude, B affects the period, and x is the variable. The period is also calculated as 2π/B.

The maximum value of a sine or cosine function is equal to the amplitude (A) when the function is in the form y = A sin(Bx) or y = A cos(Bx).

The minimum value of a sine or cosine function is equal to -A when the function is in the form y = A sin(Bx) or y = A cos(Bx).

The phase shift is the horizontal shift left or right for the graph of the function. It is determined by the value of C in the equations y = A sin(B(x - C)) or y = A cos(B(x - C)).

The frequency is the number of cycles that occur in a unit interval. It is the reciprocal of the period, calculated as 1/period.