What is the definition of csc theta ?

n a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just 'csc'.

Of the six possible trigonometric functions, cosecant, cotangent, and secant, are rarely used. In fact, most calculators have no button for them, and software function libraries do not include them.

They can be easily replaced with derivations of the more common three: sin, cos and tan. 
cosecant can be derived as the reciprocal of sine:

step-by-step explanation:

i think is g(1)=-1.

hope that i can