Lesson 16 Graphing Cosine Functions

Front

What is the amplitude of a cosine function?

Back

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

Front

How do you determine the period of a cosine function?

Back

The period of a cosine function is calculated using the formula: Period = 2π / |B|, where B is the coefficient of x in the function y = A cos(Bx).

Front

What is the midline of a cosine function?

Back

The midline is the horizontal line that runs through the middle of the graph, representing the average value of the function. It is given by y = D in the function y = A cos(Bx) + D.

Front

What are the maximum and minimum values of a cosine function?

Back

The maximum value is A + D and the minimum value is -A + D for the function y = A cos(Bx) + D.

Front

What transformations can be applied to the basic cosine function?

Back

Transformations include vertical shifts (adding D), horizontal shifts (phase shifts), reflections (changing the sign of A), and stretching/compressing (changing the value of A or B).

Front

How do you graph one cycle of a cosine function?

Back

To graph one cycle, identify the amplitude, period, midline, and max/min locations. Start at the midline, go up to the maximum, back to the midline, down to the minimum, and return to the midline.

Front

What is the effect of changing the amplitude on the graph of a cosine function?

Back

Changing the amplitude (A) affects the height of the peaks and depth of the troughs. A larger |A| results in taller peaks and deeper troughs.

Front

What is the effect of changing the period on the graph of a cosine function?

Back

Changing the period (B) affects how quickly the function completes one cycle. A larger |B| results in a shorter period, causing the graph to oscillate more frequently.

Front

What is a phase shift in cosine functions?

Back

A phase shift occurs when the graph is shifted horizontally. It is determined by the value of C in the function y = A cos(B(x - C)).

Front

How do you find the x-intercepts of a cosine function?

Back

To find the x-intercepts, set the function equal to zero and solve for x. For y = A cos(Bx) + D, solve A cos(Bx) + D = 0.