Standard Form of Sine & Cosine Graphs

Front

What is the standard form of a sine function?

Back

The standard form of a sine function is given by: 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 vertical shift.

Front

What is the standard form of a cosine function?

Back

The standard form of a cosine function is given by: 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 vertical shift.

Front

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

Back

The amplitude is the absolute value of A in the standard form y = A sin(B(x - C)) + D or y = A cos(B(x - C)) + D.

Front

What is the formula to find the period of a sine or cosine graph?

Back

Front

What does a positive value of A indicate in a sine or cosine function?

Back

A positive value of A indicates that the graph opens upwards (for sine) or starts at its maximum value (for cosine).

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What does a negative value of A indicate in a sine or cosine function?

Back

A negative value of A indicates that the graph opens downwards (for sine) or starts at its minimum value (for cosine).

Front

What is a phase shift in sine and cosine graphs?

Back

The phase shift is the horizontal shift left or right for the graph, determined by the value of C in the standard form.

Front

How do you determine the vertical shift of a sine or cosine graph?

Back

The vertical shift is determined by the value of D in the standard form, indicating how much the graph moves up or down.

Front

What is the effect of changing the value of B in the sine or cosine function?

Back

Changing the value of B affects the period of the graph; a larger B results in a shorter period.

Front

What does it mean to reflect a sine or cosine graph across the x-axis?

Back

Reflecting across the x-axis occurs when A is negative, causing the graph to invert.