I was helping someone do a trigonometry word problem, and we computed the following thing by calculator. $$\tan(33^\circ)-\tan(27.7^\circ)=0.124$$ I was pretty surprised to get a rational number back here. Does anyone have any insight as to why that happened? Is this more unlikely than I imagine? Or, do you think the textbook authors are conspiring to make things work out that way?
2026-04-06 11:16:04.1775474164
Why is $\tan(33^\circ)-\tan(27.7^\circ)=0.124$?
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Your equation is not true. It's not even close; the next few digits are
$$ 0.1243958558\ldots $$
You can see this, for example, in this wolfram alpha calculation.
Presumably, whatever calculator you used decided to round the result to the same level of precision you supplied. For example, wolfram alpha (currently) does that.