Identifying Cos Graphs

Front

What is the general shape of a cosine graph?

Back

The cosine graph has a wave-like shape, starting at its maximum value (1) when x = 0, and oscillating between 1 and -1.

Front

What is the period of the cosine function?

Back

The period of the cosine function is 2π, meaning it repeats its values every 2π units along the x-axis.

Front

How does the amplitude of a cosine graph affect its shape?

Back

The amplitude of a cosine graph determines the height of the peaks and the depth of the troughs. A larger amplitude results in taller peaks and deeper troughs.

Front

What is the effect of a phase shift on a cosine graph?

Back

A phase shift moves the graph left or right along the x-axis. For example, cos(x - π/2) shifts the graph π/2 units to the right.

Front

What does a negative cosine function indicate about the graph?

Back

A negative cosine function, such as -cos(x), reflects the graph across the x-axis.

Front

How do you identify the x-intercepts of a cosine graph?

Back

The x-intercepts of a cosine graph occur where the function equals zero, specifically at x = (2n + 1)π/2, where n is an integer.

Front

What is the relationship between the cosine function and the unit circle?

Back

In the unit circle, the cosine of an angle corresponds to the x-coordinate of the point on the circle at that angle.

Front

How does changing the frequency of a cosine graph affect its appearance?

Back

Increasing the frequency compresses the graph horizontally, resulting in more cycles within a given interval.

Front

What is the equation of a basic cosine function?

Back

The equation of a basic cosine function is y = cos(x).

Front

What is the significance of the vertical shift in a cosine graph?

Back

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