Question

The value of this is sin(2sin^-1(0.6))

Answer 1

Answer:

0.96

Step-by-step explanation:

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, sin² A + cos² A = 1 ⇒ sin² A = 1 - cos² A ⇒ sin A = √(1-cos² A) )

$1-cos^2A = 0.36$

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

$\implies cos A = 0.8$

We know that,

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

From equation (1),

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

Answer 2

$\qquad { \sin }^{ - 1} (0.8) = \theta$

$\displaystyle \qquad { \sin } \: \theta = \frac{8}{10}$

$\displaystyle \qquad \: \: \: \: \: \: \: \: \: \: = \frac{4}{5}$

$\implies \: \: \therefore \: \: \: = \sin(2 \theta)$

$\qquad \qquad = 2 \sin \theta\cos \theta$

$\displaystyle \qquad \qquad = 2 \times \frac{4}{5} \times \frac{3}{5}$

$\displaystyle \qquad \qquad = \frac{24}{25} \times \frac{4}{4}$

$\displaystyle \qquad \qquad = \frac{96}{100}$

$\displaystyle \qquad \qquad \bf = 0.96$

$\:$