Sin and Cos Graphs

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. It is always a positive value.

Front

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

Back

The period is calculated as 2π divided by the coefficient of x in the function. For example, in y = a cos(bx), the period is 2π/b.

Front

What does a vertical shift in a sine or cosine function indicate?

Back

A vertical shift moves the graph up or down. For example, in y = sin(x) + 2, the graph shifts up by 2 units.

Front

What effect does a negative sign in front of a cosine function have on its graph?

Back

A negative sign reflects the graph across the x-axis. For example, y = -cos(x) is the reflection of y = cos(x).

Front

What is the period of the function y = 4cos(5x)?

Back

The period is 2π/5.

Front

How does the coefficient in front of the sine or cosine function affect its amplitude?

Back

The coefficient represents the amplitude. For example, in y = 3sin(x), the amplitude is 3.

Front

What is the vertical shift of the function y = 4cos(0.5x + π) - 2?

Back

The vertical shift is down 2.

Front

How do you find the amplitude of the function y = -2sin(x)?

Back

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

Front

What is the period of the function y = sin(2x)?

Back

The period is π.

Front

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

Back

Phase shift refers to the horizontal shift of the graph. It is determined by the value inside the function with x.