Find the approximate value of $\sin^{-1}(0.51)$ given that $\sqrt {3}=1.7321$

Let y equal the inverse sine of x and use the derivative formula where the change in y is approximately the change in x divided by the square root of 1 minus x squared, with x initially at 0.5. The change in x is 0.01, and the square root of 1 minus 0.5 squared is the square root of 3 divided by 2, which makes the change in y equal to 0.01 multiplied by 2 divided by 1.7321, equaling 0.011541. Adding this small increment to the inverse sine of 0.5, which is pi divided by 6, gives pi divided by 6 plus 0.011541.

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