Answer:
The period is 2pi
Step-by-step explanation:
A function is said to be periodic if there exists a T for which f(x+T)=f(x). In this case, the function is f(x) =7sin^3(x).
The period of sin(x) = 2pi. Then, in this case, no matter if the sin is elevated to a power of three, the period will remain the same.
Let's prove it:
f(x) =7sin^3(0) = 0
f(0 + 2pi) = f( 2pi) = 7sin^3(2pi) = 0.
Then, there exists a T for which f(x+T)=f(x) and it's T=2pi.
