1. What is one period of the function f(x) = 120 sin(120πx).

Question

2. When does f(x) = 25 − x − sin(x) cross the x-axis?

Answer 1

sin(kx) has period 2π/k

the other requires some numeric or graphical techniques:

But you know it will be somewhere near x=25, since |sinx| <= 1 and 25-x=0 at x=25

http://www.wolframalpha.com/input/?i=25+%E2%88%92+x+%E2%88%92+sin(x)