Question 974077
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]?
<pre>
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) = {{{1/2}}};                x = 0, 2<font face="symbol">p</font>
          x = {{{pi/3}}},{{{5pi/3}}}
 
Answer: four times since we include both 0 and 2<font face="symbol">p</font>,
and the interval is given with brackets on both sides [0,2<font face="symbol">p</font>]

{{{graph(400,3000/17,-.5,6.3,-1.5,1.5,cos(x),cos(2x))}}}


Edwin</pre>