Sin and Cos Graphs

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

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 the peak (or trough). It is the coefficient in front of the sine or cosine function.

Front

What does the equation y = A sin(Bx) represent?

Back

A represents the amplitude, and B affects the period of the function. The period is calculated as 2π/B.

Front

How do you determine the period of the function y = sin(kx)?

Back

The period is calculated as 2π/k, where k is the coefficient of x.

Front

What is the effect of a negative sign in front of a cosine function, such as y = -cos(x)?

Back

A negative sign reflects the graph across the x-axis.

Front

What is the difference between sine and cosine functions?

Back

Sine functions start at the midline (0) and go up, while cosine functions start at the maximum value (A) and go down.

Front

What is the equation of the graph for a sine function with an amplitude of 2?

Back

y = 2 sin(x) represents a sine function with an amplitude of 2.

Front

What is the equation of the graph for a cosine function with a period of π?

Back

y = cos(2x) has a period of π, since the period is 2π/2 = π.

Front

How does the value of k in y = sin(kx) affect the graph?

Back

The value of k affects the frequency and period of the graph. Higher values of k result in more cycles in the same interval.

Front

What is the midline of a sine or cosine function?

Back

The midline is the horizontal line that runs through the middle of the wave, typically at y = 0 unless shifted vertically.