Sin/Cos graphs - period and midline

Front

What is the definition of Amplitude in a sine or cosine graph?

Back

Amplitude is the distance from the midline to the maximum or minimum value of the function.

Front

How do you calculate the Period of a sine or cosine function?

Back

The period is calculated using the formula: Period = \frac{2\pi}{|b|}, where b is the coefficient of x in the function.

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, representing the average value of the function.

Front

What is the effect of changing the Amplitude on the graph of a sine or cosine function?

Back

Changing the amplitude stretches or compresses the graph vertically. A larger amplitude results in taller peaks and deeper troughs.

Front

What happens to the graph of a sine or cosine function when the Period is increased?

Back

Increasing the period stretches the graph horizontally, making it take longer to complete one cycle.

Front

What is the formula for the Period of the function y = 4cos(5x)?

Back

The period is \frac{2\pi}{5}.

Front

How does a vertical translation affect the graph of a sine or cosine function?

Back

A vertical translation shifts the entire graph up or down without changing its shape.

Front

What is the relationship between the coefficients in the function y = A sin(Bx + C) + D and the graph?

Back

A represents the amplitude, B affects the period, C represents the phase shift, and D represents the vertical translation.

Front

What is the phase shift in the function y = sin(x - \frac{\pi}{2})?

Back

The phase shift is \frac{\pi}{2} to the right.

Front

What is the maximum value of the function y = 3sin(x) + 1?

Back

The maximum value is 3 + 1 = 4.