Differentiate distance with time and you get speed, differentiate speed with time and you get acceleration! Calculus is around us everyday!
I did my O-Levels and A-Levels so long ago that I cannot remember the level to which trig was studied at each stage. But, to my way of thinking, if you have a mathematical brain, then maths A-levels are easy money to get good grades!
Having looked the trig in Nav just recently, my gut instinct is that it was more A-Level than O. And given GCSEs are not quite the standard that O-Levels were (since they were designed to replace O-Levels and CSEs), I would be sceptical if the level of trigonomtery covered at GSCE is sufficient.
Cheers
Whirls