Question

Find the value of Sin^-1(0.6)

Answer 1

$\bf\underline {Given},$

$sin(2sin^{-1}(0.6))$

$Let,$

$sin^{-1}(0.6)=A -------(1)$

$\implies sin A = 0.6$

$\implies \sqrt{1-cos^2A} = 0.6 ( Since, {sin}^{2} A + {cos}^{2}A = 1 ⇒ {sin}^{2}A = 1 - {cos}^{2}A ⇒ sin A = \implies(1-{cos}^{2} A )$

$1-cos^2A = 0.36$

$cos^2A= 1-0.36 = 0.64$

$\implies cos A = 0.8$

$\bf\underline{We\: know \:that},$

$sin 2A = 2 sin A cos A = 2\times 0.6\times 0.8=0.96$

$\bf\underline{From\: equation\:(1)},$

$\implies sin 2[sin^{-1}(0.6)]=0.96$.