Question

what are the solutions to sin(t)=-1

Answer 1

are you familiar with sin curve?

Answer 2

Check out the graph of a sine wave, you'll see the same number again every time you move 2pi to the left or right. So, sin(t) = -1 technically has an infinite number of solutions. But if you know \[3 \pi/2\ = -1\] you can just keep moving 2pi to the right or left, \[3\pi/2, 7\pi/2, etc\]