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.

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

we have to approximate tan alpha by alpha for angles less than 20 degrees
20 dgrees in radians 0.349
let's find tan 0.349=0.363
percentage error=(0.349-.363)*100/(0.363)
=-3 perecent error
so for largest angle 20 degrees , the erroe is less than 10 percenr

Answer 2

Wikipedia has a good explanation with good graphs. http://en.wikipedia.org/wiki/Small-angle_approximation