Graphs of Trig Functions Review

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph. It indicates how far the graph rises and falls.

Front

What is the period of a trigonometric function?

Back

The period is the length of one complete cycle of the graph. For sine and cosine functions, the standard period is 2π.

Front

What is the midline of a trigonometric function?

Back

The midline is a horizontal line that represents the average value of the function. It is the line around which the graph oscillates.

Front

What does a vertical dilation of a function do?

Back

A vertical dilation stretches or compresses the graph vertically. For example, g(t) = k * f(t) where k > 1 stretches the graph, and 0 < k < 1 compresses it.

Front

What does a horizontal dilation of a function do?

Back

A horizontal dilation stretches or compresses the graph horizontally. For example, g(t) = f(bt) where b > 1 compresses the graph, and 0 < b < 1 stretches it.

Front

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

Back

A vertical translation shifts the graph up or down without changing its shape. For example, g(t) = f(t) + k shifts the graph up if k > 0 and down if k < 0.

Front

How does a horizontal translation affect the graph of a function?

Back

A horizontal translation shifts the graph left or right. For example, g(t) = f(t - h) shifts the graph right if h > 0 and left if h < 0.

Front

What is the effect of changing the coefficient of sine or cosine in a function?

Back

Changing the coefficient affects the amplitude of the function. For example, in g(t) = A * sin(t), A determines how high and low the graph goes.

Front

What is the effect of changing the argument of sine or cosine in a function?

Back

Changing the argument affects the period of the function. For example, in g(t) = sin(bt), the period is 2π/b.

Front

What is the general form of a sine function?

Back

The general form is g(t) = A * sin(B(t - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.