Sine and Cosine Graphs

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is always a positive value.

Front

How do you determine the period of a sine or cosine function?

Back

The period is calculated as 2π divided by the absolute value of the coefficient of x in the function.

Front

What is the formula for the period of y=4cos5x?

Back

The period is 2π/5.

Front

What does a negative sign in front of a cosine function indicate?

Back

It indicates a reflection of the graph across the x-axis.

Front

What is a phase shift in trigonometric functions?

Back

A phase shift is a horizontal shift left or right of the graph, determined by the value of the horizontal translation in the function.

Front

What is the midline of a sine or cosine graph?

Back

The midline is the horizontal line that runs through the middle of the graph, representing the average value of the function.

Front

How does changing the amplitude affect the graph of a sine or cosine function?

Back

Increasing the amplitude stretches the graph vertically, while decreasing it compresses the graph vertically.

Front

What is the effect of changing the period of a sine or cosine function?

Back

Changing the period affects the frequency of the waves; a shorter period results in more cycles in a given interval.

Front

What is the general form of a sine function?

Back

The general form is y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline.