# How do you calculate the sin ^ -1 (.6075) ?

Nov 29, 2015

$\theta = {37.41}^{\circ} , {142.59}^{\circ}$

#### Explanation:

Since $0.6075$ is not an angle in a special triangle, we have to use a calculator:

$\sin \theta = \left(0.6075\right)$
$\theta = {\sin}^{-} 1 \left(0.6075\right)$
$\theta \approx {37.41}^{\circ}$

However, since the CAST rule states that sine is positive in quadrants $1$ and $2$, our answer should also include the other principal angle in quadrant $2$.

To find the other angle, we do ${180}^{\circ} - {37.41}^{\circ}$ to find the principal angle in quadrant $2$:

${180}^{\circ} - {37.41}^{\circ}$
$\approx {142.59}^{\circ}$