You can put this solution on YOUR website! How many times does the graph of f(x) = cos(x) intersect the graph of g(x) = cos(2x) in the interval [0, 2 pi]?
To find where they intersect we set f(x) = g(x)
cos(x) = cos(2x)
cos(x) = 2cosē(x) - 1
0 = 2cosē(x) - cos(x) - 1
We factor the right side
0 = [2cos(x) + 1][cos(x) - 1]
Use the zero-factor property:
2cos(x) + 1 = 0; cos(x) - 1 = 0
2cos(x) = 1; cos(x) = 1
cos(x) = ; x = 0, 2p
x = ,
Answer: four times since we include both 0 and 2p,
and the interval is given with brackets on both sides [0,2p]
Edwin
