Chapter 1, Problem 36AP

In physics, it is important to use mathematical approximations. (a) Demonstrate that for small angles (< 20°)

$\tan \alpha \approx \sin \alpha \approx \alpha =\frac{\pi \alpha ’}{180°}$

where α is in radians and α’ is in degrees. (b) Use a calculator to find the Largest angle for which tan α may be approximated by α with an error less than 10.0%.