For question one, the easiest way to start is with t=0, so, everything inside the sine function will equal 0, and sin(0) is 0, so that is our starting point. Then, consider the following:
sin(pi/2) = 1
sin(pi) = 0
sin(3pi/2) = -1
sin(2pi) = 0
(You need to know the unit circle)
Then, we see that t=4 is a solution since the 4 times a half is 2, exactly what we need for 2 (pi). Also because it goes around the unit circle.
Problem 2 you just need the period formula. It is [2pi / b] and b is the number in front of t. So we get (2pi / (2pi / 15)). Simplifying leads to 30pi over 2pi which is just 15. Thus the period is 15 units
Lastly, Problem 3 asks for the inverse of a period since the frequency is 1 over the period. Applying the method from the last problem:
2pi / 524pi which simplifies to 1 over 262 is the period.
Now flipping 1 over 262 gives the frequency, which is just 262 by itself
Hope this long explanation helped