Transformations of Trig Functions

Front

What is the period of the function \(y = \cos(kx)\)?

Back

The period is given by \(\frac{360}{|k|}\).

Front

What is the amplitude of the function \(y = A \cos(x)\)?

Back

The amplitude is \(|A|\), which measures the distance from the midline to the maximum or minimum of the function.

Front

What does the parameter 'b' represent in the function \(f(x) = A \sin(bx) + D\)?

Back

The parameter 'b' affects the period of the function, calculated as \(\frac{360}{|b|}\).

Front

How does a vertical translation affect the graph of a trigonometric function?

Back

A vertical translation shifts the graph up or down by the value of the constant added or subtracted.

Front

What is the midline of the function \(y = A \sin(bx) + D\)?

Back

The midline is the horizontal line at \(y = D\), which represents the average value of the function.

Front

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

Back

It reflects the graph across the x-axis.

Front

What is the period of the function \(y = \sin(4x)\)?

Back

The period is \(\frac{360}{4} = 90\) degrees.

Front

What is the amplitude of the function \(y = -2 \sin(x)\)?

Back

The amplitude is \(|-2| = 2\).

Front

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

Back

If the graph starts at the midline and goes up, it is a sine function; if it starts at a maximum or minimum, it is a cosine function.

Front

What is the effect of changing the value of 'A' in the function \(y = A \cos(x)\)?

Back

Changing 'A' alters the amplitude of the graph.