Answer
0.515155 (using the principle of approx. calculations & small errors)
Steps
Let y equals sin(x)
dy equals cos(x) dx
Sin(30 deg.) equals (1/2) equals 0.5
Hence value sin(31 deg.) Equals. Sin(30 deg) plus Cos(30) x dx
Where dx eq 0.0175
0.5 plus (0.8660)x(0.0175)
Equals 0.515155
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