f(t)=21.8cos(2.85t+0.52) and g(t)=18.7cos(2.85t+1.43)

Question

What the frequency of both functions?

f(t)=21.8cos(2.85t+0.52) and g(t)=18.7cos(2.85t+1.43)

Answer 1

The period of the argument is 2π, because the cosine starts at 1 when the argument is zero and returns to this point when the argument is 2π. The frequency is 1 cycle in the period.

Comparing cos(2x) with cos(x) we can see that the function produces 2 cycles where before there was only one. A phase shift in the argument (the constant term) does not affect the frequency, so since the coefficient of t is the same for both functions the frequency is 2.85.