Question

In physics it is important to use mathematical approximations. Demonstrate that for small angles (< 20°) the following relationship is true where α is in radians and α' is in degrees.
tan(alpha)~= sin(alpha) ~= alpha = (pi*alpha')/(180 deg)
Use a calculator to find the largest angle for which tan α may be approximated by α with an error less than 10.0%

Answer 1

These things are called the "small angle approximations", or at least they were when I was at college. They are useful ways of simplifying real world calculations and making life easier. The point is that if an approximated answer is close enough for one's purposes then that is OK. The skill is in knowing what level of accuracy is required. So as the old joke goes: to a mathematician, pi is the ratio of the circumference of a circle to its diameter; to a physicist, pi is 3.14159 plus or minus 0.000005; tp an engineer, pi is about 22/7; to a builder, pi is 3; and to a child: "Pie is apple!"