sin-1(1.04)

There are no real solutions to this.

$$-1\le sin\theta \le 1$$

sin-1(1.04) ?

If 1.04 is a complex number z:

$$\\ \small{\text{ $ \boxed{ \sin^{-1}(z) = -i\cdot \log\left(\sqrt{1-z^2}+i\cdot z \right) \qquad $Complex logarithm $\log{(z)} = \ln{(|z|)}+i\cdot \varphi } $ }}\\\\ \small{\text{We have $z = 1.04$}}\\ \small{\text{ \sin^{-1}(z)=sin^{-1}(1.04) = -i\cdot \log\left(\sqrt{1-(1.04)^2}+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \log\left(\sqrt{1-(1.04)^2}+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \log\left(\sqrt{ -0.0816 }+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \log\left(\sqrt{0.0816}\cdot \sqrt{-1}+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \log\left(\sqrt{0.0816}\cdot i+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \log\left(0.28565713714\cdot i+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \log\left(0.28565713714\cdot i+i\cdot 1.04 \right) $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \mathbf{ \log{\left( 1.32565713714 \cdot i \right)} } $}}\\\\ \small{\text{ a+b\cdot i = \mathbf{1.32565713714 \cdot i } \qquad a= 0 $ and $ b = 1.32565713714 $}}\\ \small{\text{ $\textcolor[rgb]{0,0,1}{|1.32565713714 \cdot i|} = \sqrt{a^2+b^2} = \sqrt{0^2+1.32565713714^2} = \textcolor[rgb]{0,0,1}{1.32565713714} $}}\\ \small{\text{ $\varphi = \tan^{-1}{ \left(\dfrac{1.32565713714}{0} \right) } \quad \Rightarrow \quad \varphi = \textcolor[rgb]{1,0,0}{\dfrac{\pi}{2}} $}} \\\\ \small{\text{ $\log{\left( 1.32565713714 \cdot i \right)} = \ln{ ( \textcolor[rgb]{0,0,1}{ 1.32565713714 } ) } + i \cdot \textcolor[rgb]{1,0,0}{ \dfrac{\pi}{2} } $}}\\\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \left( \ln{ ( 1.32565713714 ) } + i \cdot \dfrac{\pi}{2} \right) \quad \ln{ ( 1.32565713714 ) } = 0.28190828905 $}}\\ \small{\text{ sin^{-1}(1.04) = -i\cdot \left( 0.28190828905 + i \cdot \dfrac{\pi}{2} \right) $}}\\\\ \small{\text{ sin^{-1}(1.04) = -i\cdot 0.28190828905 - i^2 \cdot \dfrac{\pi}{2} \right) \quad | \quad \boxed{i^2=-1} $}}$$

$$\\ \small{\text{ $ sin^{-1}(1.04) = \dfrac{\pi}{2} - 0.28190828905 \cdot i $}}\\ \small{\text{ $ sin^{-1}(1.04) = 1.57079632679 - 0.28190828905 \cdot i $}}\\$$

sin-1(1.04) =1.0816