Question 1206253
let x = theta.
equation is 4cos(x) = 1 + 2cos(x)
subtract 2cos(x) from both sides of the equation to get:
2cos(x) = 1
divide both sides of the equation by 2 to get:
cos(x) = 1/2
cosine is positive in quadrants 1 and 4.
in quadrant 1, x = arccos(1/2) = pi/3.
the equivalent angle in the fourth quadrant is 2pi - pi/3 = 5pi/3.
the graph of both equations is shown in below.
4cos(x) = 1 + 2cos(x) where the graph of both equations intersect in the interval (0,2pi).


<img src = "http://theo.x10hosting.com/2024/022503.jpg">


translating to degrees.
0 radians * 180/pi = 0 degrees.
2pi radians * 180/pi = 360 degrees.
pi/3 radians * 180/pi = 60 degrees.
5pi/3 radians * 180/pi = 300 degrees.