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%.

Question

Physics

Kenley Webster

24 March, 21:27

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%.

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Dixie Kelley · Answer 1

We are required in this problem to approximate tan α which α is less than 20 degrees.

In radians 20degrees is equal to 0.349; find tan 0.349=0.363

percentage error = (0.349-.363) * 100 / (0.363) = - 3 percent error so for largest angle 20 degrees, the error is less than 10 percent