Find the value of x if (arc x) = 2 4 : - Vidyadip

MCQ

Find the value of $x$ if $ \sin (\text{arc} \sin \text{x}) = \frac {\sqrt {2}}{4}:$

✓
$ \frac {\sqrt {2}}{4}$
B
$ \frac {\sqrt {2}}{6}$
C
$ \frac {\sqrt {6}}{4}$
D
$ \frac {\sqrt {2}}{3}$

✓

Answer

Correct option: A.

$ \frac {\sqrt {2}}{4}$

Given, $ \sin \text{arc} \sin { \text{x} } =\frac { \sqrt { 2 } }{ 4 } =\frac { 1 }{ 2\sqrt { 2 } }$
$ \therefore \text{arc}\sin { \text{x} } =\text{arc}\sin \left (\frac {1}{2\sqrt2}\right)=0.36136$
$ \therefore \text{x}=\sin(0.36136)=\frac { 1 }{ 2\sqrt { 2 } }$

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