Can anyone explain how to get to the following solution without using a calculator:
$$\arctan(\frac{-10}{-10√3}) = \frac{π}{6}$$
?
2026-04-04 14:11:19.1775311879
solving a fraction without calculator
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First the obvious: 10/10sqrt(3)= 1/sqrt(3). "Tangent" in a right triangle is "opposite side over near side" so we have a right triangle with legs of length 1 and sqrt(3). By the Pythagorean theorem, the hypotenuse has length c, given by $c^2= 1+ 3= 4$ so c= 2. If we put two such triangles together, along their sqrt(3) sides, we have a triangle with sides 2, 2, and, 1+ 1= 2- an equilateral triangle. Each angle is 180/3= 60 degrees or pi/3 radians. The original triangle is half of that- the angle is (pi/3)/2= pi/6 radians.