Why is tan (pi/3) - sqrt (3) ? Without a calculator.

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Answer 1 · 2018-03-01T02:29:55

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#tan(pi/3) = sin(pi/3) / cos(pi/3)#

Using the unit circle/30 60 90 triangle properties,

#sin(pi/3) = sqrt(3)/2#
and
#cos(pi/3) = 1/2#

therefore #tan(pi/3) = (sqrt(3)/2)/ (1/2)#

Then simplify by multiplying the top and the bottom of the fraction by 2 to get:

#2/2 * (sqrt(3)/2)/ (1/2) = sqrt(3)/1 = sqrt3#

So,

#tan (pi/3) - sqrt (3)#

# sqrt (3) - sqrt (3)#

#0#