How do you find the exact value of ${sin}^{- 1} (sin (\frac{π}{6}))$ $sin^-1(sin(pi/6))$ ?

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How do you find the exact value of ${sin}^{- 1} (sin (\frac{π}{6}))$ $sin^-1(sin(pi/6))$ ?

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Answer 1 · 2016-07-05T18:56:24

$\frac{π}{6} .$ $pi/6.$

Explanation:

If $f^{- 1}$ $f^-1$ is the inverse fun. of a fun. $f$ $f$ , then, by defn., $f^{- 1} o f (x) = f^{- 1} (f (x) = x$ $f^-1of(x)=f^-1(f(x)=x$ and, $f o f^{- 1} (x) = f (f^{- 1} (x) = x .$ $fof^-1(x)=f(f^-1(x)=x.$

Clearly, ${sin}^{- 1} (sin (\frac{π}{6})) = \frac{π}{6}$ $sin^-1(sin(pi/6))=pi/6$

Otherwise
Recall that $sin (\frac{π}{6}) = \frac{1}{2} .$ $sin(pi/6)=1/2.$ sin^-1(sin(pi/6)) = sin^-1(1/2)=pi/6#

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How do you find the exact value of ${sin}^{- 1} (sin (\frac{π}{6}))$ $sin^-1(sin(pi/6))$ ?

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How do you find the exact value of ${sin}^{- 1} (sin (\frac{π}{6}))$ $sin^-1(sin(pi/6))$ ?