How do you evaluate ${sin}^{- 1} (\frac{1}{2})$ $sin^-1(1/2)$ without a calculator?

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How do you evaluate ${sin}^{- 1} (\frac{1}{2})$ $sin^-1(1/2)$ without a calculator?

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Answer 1 · 2016-09-03T19:09:14

By Defn. of ${sin}^{- 1}$ $sin^-1$ function, ${sin}^{- 1} x = θ, | x | \leq 1 \Leftrightarrow sin θ = x, θ \in [- \frac{π}{2}, \frac{π}{2}]$ $sin^-1 x=theta, |x| le1 iff sin theta=x, theta in [-pi/2,pi/2]$ .

As $sin (\frac{π}{6}) = \frac{1}{2}, &, \frac{π}{6} \in [- \frac{π}{2}, \frac{π}{2}], {sin}^{- 1} (\frac{1}{2}) = \frac{π}{6}$ $sin (pi/6)=1/2, &, pi/6 in [-pi/2,pi/2], sin^-1 (1/2)=pi/6$ .

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How do you evaluate ${sin}^{- 1} (\frac{1}{2})$ $sin^-1(1/2)$ without a calculator?

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