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Period of a Vector Function

I need assistance finding the period of a vector valued function. The function is of the form

cos^2(2T)+Sin^2(3t) + cos(2t-pi/2)

I remember doing something like this back in pre calc where the period was 2pi/b but the functions were not vectors. How would I proceed from here? Any help is appreciated.

Solution Summary

The period of a vector function is investigated. The solution is detailed and well presented.