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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.TF.A.4

Front

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

Back

The period is 2π/5.

Tags

CCSS.HSF.TF.A.4

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E