How do you evaluate #arccos(sqrt3/2)# without a calculator?

1 Answer
Dec 27, 2016

#arccos(sqrt(3)/2)=30^@ (=pi/6 " radians")#

Explanation:

If we split an equilateral triangle (in which all interior angles #=60^@ or pi/3 " radians"#) into two triangles as indicated:
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we will get an angle #=(60^@)/2=30^@# whose #cos# is #sqrt(3)/2#

(Note that there is also the angle #330^@# which gives this #sqrt(3)/2# ratio, but by the standard definition of #cos^(-1)# as a function we are restricted to the range #[0,pi]#