Why isn't the period 15 seconds?
I recommend you take some time to review the basics of trig graphs ...
Graphing Trigonometric Functions
I'll give my best go at it...
Uh 19 is half of 38, so it would go up 19 and down 19. Would it matter if it was -19 or positive 19?
Also, why is it cosine instead of sine? Would it matter since they are just the same graph with different translations?
2pi is one revolution, times t number of seconds, and it's divided by 15 because a revolution happens every 15 seconds.