# How do you calculate sin ( sin^ -1 ( 3/8))?

May 20, 2018

color(purple)(=> 0.375529^c or color(brown)(21.5^@

#### Explanation:

sin (sin ^-1 (3/8)

${\sin}^{-} 1 \left(\frac{3}{8}\right) = 0.384397$

$\implies \sin \left(0.384397\right)$

color(purple)(=> 0.375529^c or color(brown)(21.5^@

May 24, 2018

$\sin \arcsin \left(\frac{3}{8}\right) = \frac{3}{8}$

#### Explanation:

I never use the $- 1$ power notation for the inverse trig functions -- it's awful.

I treat $\arcsin \left(x\right)$ as a multivalued expression, all the angles whose sine is $x .$

Even though $\arcsin \left(x\right)$ is multivalued, there's only one value for it's sine,

$\sin \arcsin x = x$

Here

$\sin \arcsin \left(\frac{3}{8}\right) = \frac{3}{8}$