Transformations of Sine & Cosine

Front

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

Back

The period can be found using the formula \( \frac{2\pi}{b} \), where \( b \) is the coefficient of the variable inside the function.

Front

At what point does the graph of \( y = \cos x \) begin?

Back

The graph of \( y = \cos x \) begins at the point (0, 1).

Front

What is the period of the graphs \( y = \sin x \) and \( y = \cos x \)?

Back

The period of both \( y = \sin x \) and \( y = \cos x \) is \( 2\pi \).

Front

At what point does the graph of \( y = \sin x \) begin?

Back

The graph of \( y = \sin x \) begins at the point (0, 0).

Front

What effect does a negative value of \( A \) have in the function \( y = A \sin[B(x-C)]+D \)?

Back

A negative value of \( A \) causes a reflection of the graph across the X-axis.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the absolute value of \( A \) in the function \( y = A \sin[B(x-C)]+D \) and represents the maximum distance from the midline to the peak.

Front

How does the value of \( B \) affect the period of the sine and cosine functions?

Back

The value of \( B \) affects the period of the function, with the period being calculated as \( \frac{2\pi}{|B|} \).

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, determined by the value of \( D \) in the function \( y = A \sin[B(x-C)]+D \).

Front

What does the phase shift refer to in the sine and cosine functions?

Back

The phase shift refers to the horizontal shift of the graph, determined by the value of \( C \) in the function \( y = A \sin[B(x-C)]+D \).

Front

What is the range of the sine and cosine functions?

Back

The range of both sine and cosine functions is from -1 to 1, assuming no vertical shifts.