How does one come up with the cosine of a degree?

Answer 1

The easiest way to do this is to use a calculator or a cosine table. If you do not have a calculator, you must try one of several other options. If you know the sine or other trigonometric value of the angle, you can use trig identities. Some angles have good cosines, like 0, 30, 45, 60, 90, and so on. These values are known, and should be memorized. Cos(0) = 1, cos(30) = SQRT(3)/2, cos(45) = SQRT(2)/2, cos(60) = 1/2, and cos(90) = 0. The list continues, but I won't go on here. You may be able to use the angle addition formulas or half or double angle formulas to find the value of your angle. If this still doesn't work, you could approximate qualitatively by looking at a cosine curve, or you could use calculus methods, like Euler's method or a Taylor or Maclauren series to approximate the value. I won't go into detail here, but you can look up any of these topics on Google or Wikipedia.