Physics Homework Help!!!???

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.

tan(α)~= sin(α) ~= α = (pi*α')/(180 deg)

Use a calculator to find the largest angle for which tan α may be approximated by α with an error less than 10.0%.

α' = ????

Answer 1

tan x approximated as x, where x is radians.

trying different angles in radians,

tan .5 = 0.5463 close to 10%

tan .52 = 0.5726 = (.52)( 1.101)

close enough

.52 rad = 29.8 degrees

.

Answer 2

0 cuz 10%-10%=0DUHHHHHHHHHHHH!!!!!!!!!!!!!!!!!...

Answer 3

either use a table to find the numeric values of all angles 0 to 90,

or use an existing table.  From there, evaluate &quot;a&quot; and see where it starts to deviate more than 10%

good luck