How do you solve the inverse trig function arcsin(sin5π6)?

1 Answer
May 20, 2015

When 1x1, arcsin(x) is defined as the value θ

in the range π2θπ2 such that sinθ=x.

The value 5π6 does not fall into this range.

Instead we find:

π2<5π6<π

Use the equality sin(πθ)=sinθ and note that

5π6=ππ6

So sin(π6)=sin(ππ6)=sin(5π6)

So arcsin(sin(5π6))=π6