Question 971541
we'll do this in degrees and then translate to radians.


it's easier to show.


cos(2x) = .5


find cos^-1(.5) and you get 2x = 60 degrees.


that means that x is equal to 30 degrees.


the period of x is equal to 180 degrees because the frequency of x is equal to 2.


within that period of 180 degrees, you have 4 quadrants.


cosine is positive in the first and fourth quadrant.


30 degrees is in the first quadrant.


180 - 30 = 150 degrees is in the fourth quadrant.


within a 360 degree interval, you will get two full cycles of cosine(2x).


the cosine will be .5 at 30, 150, 30 + 180, 150 + 180.


that equates to 30, 150, 210, 330 degrees.


i'll show you the graph in degrees and then translate to radians.


<img src = "http://theo.x10hosting.com/2015/052101.jpg" alt="$$$" </a>


here's the same graph in radians.
look under the graph for further comments.


<img src = "http://theo.x10hosting.com/2015/052103.jpg" alt="$$$" </a>


instead of an interval from 0 to 360, you have an interval from 0 to 2pi.


conversion factor from degress to radians is radians = degrees * pi / 180.


30 degrees would be equal to 30/180 * pi which is equal to pi/6.


150 degrees would be equal to 150/180 * pi which is equal to 5pi/6.


210 degrees would be equal to 210/180 * pi which is equal to 7pi/6.


330 degrees would be equal to 330/180 * pi which is equal to 11pi/6.