Writing Sine and Cosine Functions From Graphs Using A, B and D

Front

What is the general form of a sine function?

Back

Front

What does the amplitude of a sine or cosine function represent?

Back

Front

How do you determine the vertical shift (D) in a sine or cosine function?

Back

The vertical shift (D) is determined by the constant added or subtracted from the sine or cosine function. It shifts the graph up or down.

Front

What is the period of a sine or cosine function?

Back

Front

How does the value of B affect the graph of a sine or cosine function?

Back

The value of B affects the frequency and period of the function. A larger value of B results in a shorter period (more cycles in a given interval), while a smaller value results in a longer period.

Front

What is the difference between sine and cosine functions?

Back

Front

How do you write the equation of a sine function given its amplitude and vertical shift?

Back

Front

What is the maximum value of a sine function?

Back

The maximum value of a sine function is equal to the amplitude A, which occurs at the peaks of the graph.

Front

What is the minimum value of a cosine function?

Back

The minimum value of a cosine function is equal to -A + D, which occurs at the troughs of the graph.

Front

How do you find the amplitude from a graph of a sine or cosine function?

Back

The amplitude can be found by measuring the distance from the midline to the maximum or minimum point of the graph.