# Problem: In physics it is important to use mathematical approximations. (a) Demonstrate that for small angles (&lt;20°): tan α ≈ sin α ≈ α = πα′/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%.

###### Problem Details

In physics it is important to use mathematical approximations. (a) Demonstrate that for small angles (<20°): tan α ≈ sin αα = πα′/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%.