Sine and Cosine Graphs Test Review

The period is the distance along the x-axis for one complete cycle of the wave. For sine and cosine functions, the period is given by the formula: Period = 2π / |B|, where B is the coefficient of x in the function.

The graph of cosine begins at the point (0, 1).

A negative A value causes a reflection across the X-axis.

The graph that starts at (0, 1) represents the cosine function.

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is given by the absolute value of A in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

The midline is the horizontal line that runs through the middle of the graph, calculated as y = D in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Changing the value of B affects the period of the graph. A larger value of B results in a shorter period, while a smaller value of B results in a longer period.

The phase shift is the horizontal shift left or right for the graph, determined by the value of C in the function y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

The range of a sine or cosine function is the set of possible output values, which is from -|A| + D to |A| + D.

Changing the value of D shifts the graph vertically up or down, affecting the midline.