Trigonometry and their reciprocal

I know sin theta=opp/hyp , cos theta= adj/ hyp and tan theta= opp/adj

I would like to know how are their respective reciprocal functions derived, step by step.

How is sin theta = (opp/ hyp) = cosec theta (hyp/opp)?
And for the rest?

this is by definition , its a trigonometry law.

this webpage may help you understand better , trigonometry by example

http://www.mathsandstats.com/maths/trigo…

There is no derivation.

Think about it this way. A guy invents trigonometry and says whenever someone divides the opp/hyp, we will call it, sine, because my daughter is named sine. And someone said so what should we call it when hyp/opp, then they said we'll call it cosecant, because I want to name it after my dog.

It's just a name. Nothing more. No need to stress yourself.