If 0 ≤ x ≤ 2π, which equation is a line of symmetry for the graph of y = cos x?
x = 0
x = 2π
x = π
y = 0
y=0 is not the y-axis.
And anyway, in the stated domain, x=pi is the axis of symmetry.
To find the line of symmetry for the graph of the equation y = cos x, we need to consider the period of the cosine function.
The cosine function has a period of 2π, which means that the graph of y = cos x repeats itself every 2π units.
Since the cosine function is an even function, the graph is symmetric about the y-axis. This means that the line of symmetry for the graph is the y-axis, which is represented by the equation x = 0.
Therefore, the correct choice is:
x = 0
To determine which equation represents a line of symmetry for the graph of y = cos x, we need to understand what symmetry means in terms of a graph.
A graph has a line of symmetry if it can be folded over that line in such a way that the two halves are identical. In this case, we need to find an equation that represents a vertical line that divides the graph of y = cos x into two identical halves.
The graph of y = cos x represents a cosine function, which is a periodic function with a period of 2π. This means the graph repeats every 2π.
In the given range 0 ≤ x ≤ 2π, the graph of y = cos x starts at (0, 1), reaches a minimum at (π, -1), returns to (2π, 1), and then repeats.
To find the line of symmetry, we need to find the x-coordinate at which the graph is symmetric. Since the graph is symmetric about the y-axis, the line of symmetry will be at the x-coordinate halfway between the first and last points of the graph in the given range.
The first point is (0, 1) and the last point is (2π, 1). The x-coordinate halfway between these two points is π. Therefore, the line of symmetry for the graph of y = cos x in the given range is x = π.
So, the correct equation that represents a line of symmetry for the graph of y = cos x in the range 0 ≤ x ≤ 2π is x = π.
y = 0
The graph of y = cos x is symmetrical about the y axis.