Answer:
x ∈ {1.047198, 1.318116, 4.965069, 5.235988}
Step-by-step explanation:
To find the values of cos(x), you solve this like you would any other quadratic equation. Factoring gives ...
(4cos(x) -1)(2cos(x) -1) = 0
which has solutions that make these factors zero:
cos(x) = 1/4
cos(x) = 1/2
Using the inverse cosine function, we have ...
x = ±arccos(1/4) +2kπ
x = ±arccos(1/2) +2kπ = ±π/3 +2kπ
The four smallest positive solutions will be the positive values with k=0 and the negative values with k=1.
x ∈ {1.047198, 1.318116, 4.965069, 5.235988}
