[Math] How to calculate cos, sine, etc. Without a calculator

linear algebratrigonometry

I am currently studying computer science at university, and one of this semesters courses I am taking is linear algebra and calculus II. Every week there is a graded quiz, and a mid and end of semester exam. We are not allowed to use calculators in any of these.

Today in the quiz, I failed to get an answer to one of the questions regarding the angle between two vectors, because I had to work out $\cos x = \frac2{2\sqrt\frac43}$. But I had no idea what angle that resulted in.

I was just wondering if anyone had some tips as to how best to solve these problems in the future?

Best Answer

Well, surely the first step is to write that as $\cos(x) = \frac{\sqrt{3}}{2}$. Could you have done it then?

At that point, it's about remembering a common triangle.