Sine and Cosine Graph

Front

What is the period of a sine or cosine graph?

Back

The period of a sine or cosine graph is the distance along the x-axis required for the graph to complete one full cycle. For the standard sine and cosine functions, the period is 2π.

Tags

CCSS.HSF.TF.A.4

Front

What is the amplitude of a sine or cosine graph?

Back

The amplitude of a sine or cosine graph is the maximum distance from the midline (equilibrium position) to the peak (or trough) of the graph. It is always a positive value.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the amplitude from the equation of a sine or cosine function?

Back

The amplitude can be determined from the equation of the function in the form y = A sin(Bx) or y = A cos(Bx), where |A| represents the amplitude.

Tags

CCSS.HSF-IF.C.7E

Front

What is the starting point of the cosine graph?

Back

The graph of cosine begins at the point (0, 1) when the function is in its standard form.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between sine and cosine graphs?

Back

The sine graph starts at the origin (0,0) and oscillates between -1 and 1, while the cosine graph starts at (0,1) and also oscillates between -1 and 1.

Tags

CCSS.HSF-IF.C.7E

Front

What is the phase shift in a sine or cosine graph?

Back

The phase shift is the horizontal shift left or right for the graph of a sine or cosine function, determined by the value of B in the equation y = A sin(B(x - C)) or y = A cos(B(x - C)).

Tags

CCSS.HSF-IF.C.7E

Front

What is the vertical shift in a sine or cosine graph?

Back

The vertical shift is the amount the graph is moved up or down from its standard position, determined by the value of D in the equation y = A sin(Bx) + D or y = A cos(Bx) + D.

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, making the peaks and troughs higher and lower, while decreasing the amplitude compresses the graph.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

Changing the period affects the frequency of the oscillations; a shorter period results in more cycles within a given interval, while a longer period results in fewer cycles.

Tags

CCSS.HSF-IF.C.7E

Front

What is the range of the sine and cosine functions?

Back

The range of both sine and cosine functions is [-1, 1], meaning the output values will always fall within this interval.

Tags

CCSS.HSF.TF.A.4