Question

find the value of cos(sin^-1 2/3)
​

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ \cos \bigg( { \sin}^{ - 1} \: \frac{2}{3} \bigg)}$

EVALUATION

Let

$\displaystyle \sf{ \theta = { \sin}^{ - 1} \frac{2}{3} }$

Then we have to find the value of cos θ

Now

$\displaystyle \sf{ \theta = { \sin}^{ - 1} \frac{2}{3} }$

$\displaystyle \sf{ \implies \: \sin \theta = \frac{2}{3} }$

$\displaystyle \sf{ \implies \: \cos \theta = \sqrt{1 - \frac{4}{9} } }$

$\displaystyle \sf{ \implies \: \cos \theta = \sqrt{ \frac{5}{9} } }$

$\displaystyle \sf{ \implies \: \cos \theta = \frac{ \sqrt{5} }{3} }$

Thus we get

$\displaystyle \sf{ \cos \bigg( { \sin}^{ - 1} \: \frac{2}{3} \bigg) = \frac{ \sqrt{5} }{3} }$

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