Sine and Cosine Graphs

Front

What is the definition of 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, representing the height of the wave.

Front

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

Back

The period can be found using the formula: Period = 2π/B, where B is the coefficient of x in the function.

Front

What does the graph of f(x) = 3 sin x look like?

Back

The graph is a sine wave with an amplitude of 3, oscillating between 3 and -3.

Front

How does changing the coefficient of x in f(x) = sin(Bx) affect the graph?

Back

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

Front

What is the period of the function f(x) = sin(3x)?

Back

The period is 2π/3.

Front

What is the amplitude of the function f(x) = -2 cos x?

Back

The amplitude is 2, as amplitude is always a positive value.

Front

How do you determine if a function is sine or cosine based on its graph?

Back

A sine graph starts at the midline, while a cosine graph starts at its maximum or minimum value.

Front

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

Back

It reflects the graph across the x-axis.

Front

What is the period of the function f(x) = sin(⅓ x)?

Back

The period is 6π.

Front

What is the maximum value of the function f(x) = 4 sin x?

Back

The maximum value is 4.