Small-angle approximation: Difference between revisions

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Many [[slide rule]]s – especially "trig" and higher models – include an "ST" (sines and tangents) or "SRT" (sines, radians, and tangents) scale on the front or back of the slide, for computing with sines and tangents of angles smaller than about 0.1 radian.<ref>{{cite book |title=Communications Technician M 3 & 2 |date=1965 |publisher=Bureau of Naval Personnel |page=481 |url=https://books.google.com/books?id=FYB3o7iGvb8C&pg=PA481#v=onepage&q&f=false |access-date=7 March 2025}}</ref>
 
The right-hand end of the ST or SRT scale cannot be accurate to three decimal places for both arcsine(0.1) = 5.74 degrees and arctangent(0.1) = 5.71 degrees, so sines and tangents of angles near 5 degrees are given with somewhat worse than the usual expected "slide-rule accuracy". Some slide rules, such as the K&E Deci-Lon in the photo, calibrate 0.1 to be accurate for radian conversion, at 5.73 degrees (off by nearly 0.4% for the tangent and 0.2% for the sine for angles around 5 degrees). Others are calibrated to 5.725 degrees, to balance the sine and tangent errors at below 0.3%.
 
== Angle sum and difference ==