How do you evaluate the equation $arcsin (sin (\frac{5 π}{6}))$ $arcsin(sin ((5pi)/6))$ ?

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Answer 1 · 2015-12-21T11:43:28

$arcsin (sin (\frac{5 π}{6})) = \frac{π}{6}$ $arcsin(sin((5pi)/6)) = pi/6$

$arcsin$ $arcsin$ is only defined as having a range $[- \frac{π}{2}, + \frac{π}{2}]$ $[-pi/2,+pi/2]$

$sin (\frac{5 π}{6}) = \frac{1}{2} = sin (\frac{π}{6})$ $sin((5pi)/6) = 1/2 = sin(pi/6)$

$arcsin (sin (\frac{5 π}{6})) = arcsin (\frac{1}{2}) = \frac{π}{6}$ $arcsin(sin((5pi)/6))=arcsin(1/2) = pi/6$

How do you evaluate the equation arcsin(sin ((5pi)/6))arcsin(sin(5π6))arcsin(sin ((5pi)/6))?