1. The problem statement, all variables and given/known data Hello! Surprisingly I get different results when I try to compute the inverse tangent function. My goal is to compute it both manually and using calculator in radiant mode. 2. Relevant equations My goal is to compute arctan(½) both manually and using calculator in radiant mode. 3. The attempt at a solution (1) First problem with calculator: When I try to compute arctan(½) using any online calculator, I stumble upon different results; some calculators even refuse to compute it. - https://web2.0calc.com gives me the result I see in the textbook arctan(½) = 0.463647609001 - http://calculator.tutorvista.com/arctan-calculator.html arctan(½) = 0.785... (2) Second problem - manual computation gives different answer from any of above ones: arctan(½) means that tan(θ) = ½ This means that θ can be in Quadrant I or in Quadrant III. tan(θ) = sin(θ) / cos(θ) sin(θ) = √1 - cos2(θ) (the whole expression is under square root sign, sorry for not being able to show it correctly) hence, tan(θ) = ( √1 - cos2(θ)) / cos(θ) Let cos(θ) = x, then tan(θ) = ( √1 - x2) / x = ½ Squaring both sides I get: (1 - x2) / x2 = ¼ x = +- 2/√5 Let's choose positive cos, then cos(θ) = 2/√5 ≈ 0.8944 sin(θ) = √1-cos2(θ) = √1-0.89442 ≈ 0.4472 Thus tan(θ) = 0.4472 / 0.8944 = 0.5 (without any rounding, it is strictly 0.5) Which is not 0.463647609001 (this can be rounded to 0.5, but it is not the same). Please, help me to find my mistake in manual computation. Thank you!