Question

Sin(1/2 cos^-1 3/5)

Answer 1

\[sin\left(\frac{cos^{-1}\left(\frac{3}{5}\right)}{2}\right)\]
Alright...so in degrees or radians

Answer 2

\(\cos(2x) = 1 - 2\sin^{2}(x) \implies \sin(x) = \pm\sqrt{\dfrac{1 - cos(2x)}{2}}\implies\sin(x/2) = \pm\sqrt{\dfrac{1 - cos(x)}{2}}\)

Answer 3

I wondered if that would fit. \(\sin(x/2) = \pm\sqrt{\dfrac{1 - cos(x)}{2}}\)

Answer 4

That is a beautiful simplification @tkhunny! Neat too because we could use the property:
\[cos[cos^{-1}(x)]=x\]