How do you solve the inverse trig function arcsin (sin 5pi/6)?

1 Answer
May 20, 2015

When -1 <= x <= 1, arcsin(x) is defined as the value theta

in the range -pi/2 <= theta <= pi/2 such that sin theta = x.

The value (5pi)/6 does not fall into this range.

Instead we find:

pi/2 < (5pi)/6 < pi

Use the equality sin(pi-theta) = sin theta and note that

(5pi)/6 = pi - pi/6

So sin (pi/6) = sin (pi - pi/6) = sin ((5pi)/6)

So arcsin(sin((5pi)/6)) = pi/6