We have $\sin 25°\approx 0.42.$ How to calculate $\arcsin0. 42\approx 25°$ without the help of calculator? And how does calculator evaluate the inverse functions value.
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$\begingroup$You could use the Maclauren series for arcsin:
$$\arcsin x = x+\frac{x^3}{6} + \frac{3x^5}{40}+\frac{5x^7}{112} +\cdots.$$
So $\arcsin 0.42 \approx 0.43343.$ This is in radians, so convert to degrees: $0.43343\cdot 180/\pi \approx 24.833$ degrees.
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