Trig Graphing: Where Are We Now?

Front

What is the amplitude of a cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. For the function f(x) = -3cos x, the amplitude is 3.

Front

Define amplitude in the context of sine and cosine graphs.

Back

Amplitude represents half the distance between the maximum and minimum values of the graph.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

How does a negative amplitude affect the cosine graph?

Back

A negative amplitude reflects the graph across the midline, inverting its peaks and troughs.

Front

What is the period of a cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the graph. For y = cos(Bx), the period is 2π/|B|.

Front

What does the vertical shift (D) do to a cosine graph?

Back

The vertical shift moves the entire graph up or down by D units.

Front

How do you determine the maximum and minimum values of a cosine function?

Back

The maximum value is A + D and the minimum value is -A + D, where A is the amplitude and D is the vertical shift.

Front

What is the difference between sine and cosine functions?

Back

Sine functions start at the midline, while cosine functions start at the maximum value.

Front

What is the effect of changing the value of B in the function y = A cos(Bx)?

Back

Changing B affects the frequency and period of the graph. A larger B results in a shorter period.

Front

How do you identify the graph of a cosine function?

Back

Look for a graph that starts at its maximum value and has a wave-like pattern that repeats.