Serway & Jewett — Physics and Measurement: Problem 36

In physics, it is important to use mathematical approximations. (a) Demonstrate that for small angles (\(\alpha < 20^{\circ}\)) \[ \tan \alpha \approx \sin \alpha \approx \alpha = \frac{\pi \alpha'}{180^{\circ}} \] where \(\alpha\) is in radians and \(\alpha'\) is in degrees. (b) Use a calculator to find the largest angle for which \(\tan \alpha\) may be approximated by \(\alpha\) with an error less than \(10.0\%\).