Graphing Sine & Cosine

Front

What is the graph of y=-cos(x) characterized by?

Back

The graph of y=-cos(x) is a reflection of the cosine graph across the x-axis, starting at the point (0, 1) and oscillating between -1 and 1.

Front

What is the graph of y=-sin(x) characterized by?

Back

The graph of y=-sin(x) is a reflection of the sine graph across the x-axis, starting at the point (0, 0) and oscillating between -1 and 1.

Front

What is the period of a sine or cosine function?

Back

Front

What does the negative sign in front of a sine function indicate?

Back

The negative sign indicates a direction change, meaning the graph is reflected across the x-axis.

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, calculated as the absolute value of the coefficient in front of the sine or cosine function.

Front

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

Back

The vertical shift is the constant added or subtracted from the function, moving the graph up or down on the y-axis.

Front

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

Back

The phase shift is determined by the horizontal translation of the graph, calculated from the equation in the form y = a sin(b(x - c)) + d, where c represents the phase shift.

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.

Front

What is the effect of changing the coefficient of x in the function y=sin(kx)?

Back

Changing the coefficient k affects the frequency of the sine wave; a larger k results in more cycles within the same interval.

Front

What is the effect of changing the coefficient in front of the sine function, such as in y=Asin(x)?

Back

Changing the coefficient A affects the amplitude of the sine wave; a larger A results in a taller wave.