Question

Find the exact value of the composition.

arcos(cos pi/2)

Answer 1

These functions undo eachother. This is the definition of the inverse function. \[\large \cos^{-1}(\cos(x))=x\]and\[\large \cos(\cos^{-1}(x))=x\] For example, say you wanted to find f(g(x)) where f(x)=x+2 and g(x)=x-2

f(g(x))= (x-2) + 2 = x

Trig functions work the same way.