Question

what is the value of Sin inverse cos 3 pi by 5​

Answer 1

$\textbf{Given:}$

$sin^{-1}(cos\,\frac{3\pi}{5})$

$=sin^{-1}(cos\,108^{\circ})$

$=sin^{-1}(cos(90^{\circ}+18^{\circ}))$

$=sin^{-1}(-sin18^{\circ})$

$\text{Using,}$

$\boxed{\bf\,sin^{-1}(-x)=-sin^{-1}(x)}$

$=-sin^{-1}(sin18^{\circ})$

$\text{Using,}$

$\boxed{\bf\,sin^{-1}(sin\,x)=x}$

$=-18^{\circ}$

$=\frac{-\pi}{10}$

$\therefore\textbf{The value of \bf\,sin^{-1}(cos\,\frac{3\pi}{5}) is \bf\,\frac{-\pi}{10} }$

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Answer 2

Answer:

-π/10.................