How do you calculate sin^-1 (-0.4)?

Mar 5, 2018

$x = {203}^{\circ} 58$
$x = - {23}^{\circ} 58$, or $x = {336}^{\circ} 42$ (co-terminal)

Explanation:

${\sin}^{-} 1 \left(- 0.4\right)$ --> arc x whose sin is (-0.4)
sin x = - 0.4. Calculator gives -->
x = - 23^@58, or x = 336^@42 (co-terminal)
Unit circle gives another x that has the same sin value (- 0.4)
$x = 180 - \left(- 23.58\right) = 180 + 23.58 = {203}^{\circ} 58$