The answer is B as this is the biggest period of 4cos(x/2) and 3sin2x
In short find the individual period of both trig functions you are summing, the period of the summed functions will be the bigger of the 2.
This question is from the National University of Colombia entrance exam in 2006 (translated from Spanish).
The function y=4cos(x/2) - 3sin2x is of period:
I learned to divide the period of cos by 2π, so 2π/1/2 would be 4π I thought, and the period for the sin would be 2π/2 is π, and the least common number to divide into seems like it would make the answer 4π, but the answer sheet says D, 2π, and I can't figure out why. I have their entrance exam in two days and I need to understand all this. Please help me. Thank you